(This is the same issue as https://www.gaia-gis.it/fossil/spatialite-tools/tktview?name=3041a242d3 , at first I didn't notice there is a different ticket system per tool. Please ignore/close that other ticket.)

Spatialite 5.0.0-RC1 does not seem to respect axis order although it is supposed to be using PROJ 6 (or later), see details below.

To get the WKT of the coordinate reference systems:

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>chcp 65001
Active code page: 65001

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>projinfo -o WKT2:2019 --single-line EPSG:25832
WKT2:2019 string:
PROJCRS["ETRS89 / UTM zone 32N",BASEGEOGCRS["ETRS89",DATUM["European Terrestrial Reference System 1989",ELLIPSOID["GRS 1980",6378137,298.257222101,LENGTHUNIT["metre",1]]],PRIMEM["Greenwich",0,ANGLEUNIT["degree",0.0174532925199433]],ID["EPSG",4258]],CONVERSION["UTM zone 32N",METHOD["Transverse Mercator",ID["EPSG",9807]],PARAMETER["Latitude of natural origin",0,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",9,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.9996,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",500000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",0,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["(E)",east,ORDER[1],LENGTHUNIT["metre",1]],AXIS["(N)",north,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["unknown"],AREA["Europe - 6°E to 12°E and ETRS89 by country"],BBOX[38.76,6,83.92,12]],ID["EPSG",25832]]

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>projinfo -o WKT2:2019 --single-line EPSG:3044
WKT2:2019 string:
PROJCRS["ETRS89 / UTM zone 32N (N-E)",BASEGEOGCRS["ETRS89",DATUM["European Terrestrial Reference System 1989",ELLIPSOID["GRS 1980",6378137,298.257222101,LENGTHUNIT["metre",1]]],PRIMEM["Greenwich",0,ANGLEUNIT["degree",0.0174532925199433]],ID["EPSG",4258]],CONVERSION["UTM zone 32N",METHOD["Transverse Mercator",ID["EPSG",9807]],PARAMETER["Latitude of natural origin",0,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",9,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.9996,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",500000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",0,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["northing (N)",north,ORDER[1],LENGTHUNIT["metre",1]],AXIS["easting (E)",east,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["unknown"],AREA["Europe - 6°E to 12°E and ETRS89 by country"],BBOX[38.76,6,83.92,12]],ID["EPSG",3044]]

To get the transformation pipeline:

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>projinfo -o PROJ -s EPSG:25832 -t EPSG:3044
Candidate operations found: 1
-------------------------------------
Operation No. 1:

unknown id, Inverse of UTM zone 32N + UTM zone 32N, 0 m, World

PROJ string:
+proj=axisswap +order=2,1


SQL statements in file transform.sql:

select
AsEWKT(PointFromText('POINT(722125 6178892)', 25832)) as geometry_25832,
AsEWKT(Transform(PointFromText('POINT(722125 6178892)', 25832), 3044)) as geometry_3044_only_newSRID,
AsEWKT(Transform(PointFromText('POINT(722125 6178892)', 25832), 3044, null, 'EPSG:25832', 'EPSG:3044')) as geometry_3044_EPSG_codes,
AsEWKT(Transform(PointFromText('POINT(722125 6178892)', 25832), 3044, null, 'urn:ogc:def:crs:EPSG::25832', 'urn:ogc:def:crs:EPSG::3044')) as geometry_3044_EPSG_URNs,
AsEWKT(Transform(PointFromText('POINT(722125 6178892)', 25832), 3044, null, 'PROJCRS["ETRS89 / UTM zone 32N",BASEGEOGCRS["ETRS89",DATUM["European Terrestrial Reference System 1989",ELLIPSOID["GRS 1980",6378137,298.257222101,LENGTHUNIT["metre",1]]],PRIMEM["Greenwich",0,ANGLEUNIT["degree",0.0174532925199433]],ID["EPSG",4258]],CONVERSION["UTM zone 32N",METHOD["Transverse Mercator",ID["EPSG",9807]],PARAMETER["Latitude of natural origin",0,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",9,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.9996,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",500000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",0,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["(E)",east,ORDER[1],LENGTHUNIT["metre",1]],AXIS["(N)",north,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["unknown"],AREA["Europe - 6°E to 12°E and ETRS89 by country"],BBOX[38.76,6,83.92,12]],ID["EPSG",25832]]', 'PROJCRS["ETRS89 / UTM zone 32N (N-E)",BASEGEOGCRS["ETRS89",DATUM["European Terrestrial Reference System 1989",ELLIPSOID["GRS 1980",6378137,298.257222101,LENGTHUNIT["metre",1]]],PRIMEM["Greenwich",0,ANGLEUNIT["degree",0.0174532925199433]],ID["EPSG",4258]],CONVERSION["UTM zone 32N",METHOD["Transverse Mercator",ID["EPSG",9807]],PARAMETER["Latitude of natural origin",0,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8801]],PARAMETER["Longitude of natural origin",9,ANGLEUNIT["degree",0.0174532925199433],ID["EPSG",8802]],PARAMETER["Scale factor at natural origin",0.9996,SCALEUNIT["unity",1],ID["EPSG",8805]],PARAMETER["False easting",500000,LENGTHUNIT["metre",1],ID["EPSG",8806]],PARAMETER["False northing",0,LENGTHUNIT["metre",1],ID["EPSG",8807]]],CS[Cartesian,2],AXIS["northing (N)",north,ORDER[1],LENGTHUNIT["metre",1]],AXIS["easting (E)",east,ORDER[2],LENGTHUNIT["metre",1]],USAGE[SCOPE["unknown"],AREA["Europe - 6°E to 12°E and ETRS89 by country"],BBOX[38.76,6,83.92,12]],ID["EPSG",3044]]')) as geometry_3044_wkt2_2019,
AsEWKT(Transform(PointFromText('POINT(722125 6178892)', 25832), 3044, null, '+proj=axisswap +order=2,1', null)) as geometry_3044_Transformation_pipeline;

spatialite output:

C:\OtherPrograms\spatialite-cli-NG-RC1-win-amd64>spatialite
SpatiaLite version ..: 5.0.0-RC1        Supported Extensions:
        - 'VirtualShape'        [direct Shapefile access]
        - 'VirtualDbf'          [direct DBF access]
        - 'VirtualXL'           [direct XLS access]
        - 'VirtualText'         [direct CSV/TXT access]
        - 'VirtualNetwork'      [Dijkstra shortest path]
        - 'RTree'               [Spatial Index - R*Tree]
        - 'MbrCache'            [Spatial Index - MBR cache]
        - 'VirtualSpatialIndex' [R*Tree metahandler]
        - 'VirtualElementary'   [ElemGeoms metahandler]
        - 'VirtualKNN'  [K-Nearest Neighbors metahandler]
        - 'VirtualXPath'        [XML Path Language - XPath]
        - 'VirtualFDO'          [FDO-OGR interoperability]
        - 'VirtualGPKG' [OGC GeoPackage interoperability]
        - 'VirtualBBox'         [BoundingBox tables]
        - 'SpatiaLite'          [Spatial SQL - OGC]
PROJ version ........: Rel. 7.1.0, August 1st, 2020
GEOS version ........: 3.8.1-CAPI-1.13.3
RTTOPO version ......: 1.1.0
TARGET CPU ..........: x86_64-w64-mingw32
the SPATIAL_REF_SYS table already contains some row(s)
SQLite version ......: 3.32.3
Enter ".help" for instructions
SQLite version 3.32.3 2020-06-18 14:00:33
Enter ".help" for instructions
Enter SQL statements terminated with a ";"
spatialite> .headers ON
spatialite> .mode line
spatialite> .read transform.sql "UTF-8"
                       geometry_25832 = SRID=25832;POINT(722125 6178891.999999999)
           geometry_3044_only_newSRID = SRID=3044;POINT(722125 6178891.999999999)
             geometry_3044_EPSG_codes = SRID=3044;POINT(722125 6178891.999999999)
              geometry_3044_EPSG_URNs = SRID=3044;POINT(722125 6178891.999999999)
              geometry_3044_wkt2_2019 = SRID=3044;POINT(722125 6178891.999999999)
geometry_3044_Transformation_pipeline = SRID=3044;POINT(6178891.999999999 722125)

Only when using the transformation pipeline, the correct result is obtained.


When using PROJ to transform the coordinates, I get the following output:

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>echo 722125 6178892 | cs2cs EPSG:25832 EPSG:3044
6178892.00      722125.00 0.00

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>echo 722125 6178892 | cs2cs urn:ogc:def:crs:EPSG::25832 urn:ogc:def:crs:EPSG::3044
6178892.00      722125.00 0.00

C:\ProgramData\Microsoft\Windows\Start Menu\Programs\OSGeo4W>echo 722125 6178892 0 0 | cct +proj=axisswap +order=2,1
 6178892.0000    722125.0000        0.0000        0.0000

Sorry, changing the traditional and well established axis order will abruptly break any historical compatibility with existing databases created by earlier versions.
Absolutely out of discussion, it would disseminate chaos everywhere.