What we basically want to achieve is to import UTM coordinates that include the zone number.
and turn them into UTM coordinates without a zone number, because the CRSs in QGIS already add that.
The second one will plot correctly with UTM zone 32N selected. The first one will plot 32000000 meters too far to the East. Unfortunately most DXF files I've come across do use that full format.
What I would have loved to see is a CRS definition which automatically takes the zone number from the coordinates. But I guess that is not possible.
What might be possible, but I haven't tried that, is what Gabriel suggested. Add the "zone" as false Easting. However, that would have to be done for each zone individually again.
Now here are two work arounds for this problem.
What I settled for atm is to move the features with "Translate" like csk suggested.
It is part of the toolbox under vector geometry.
Be sure to select the correct UTM CRS before you do that. Otherwise it won't translate correctly because the input might be in degrees instead of meters.
For my example I then need to translate the layer in question by -32000000 meters in x direction. Because it is part of UTM zone 32. If you'd have complete coordinates from zone 33 then you'd have to translate it by -33000000 meters. Basically getting rid of the first two digits of the X coordinate.
Afterwards it will plot in the correct location.
The same thing can also be accomplished in the CAD software, before the export, with the "MOVE" command. In Draftsight select everything you need and just enter MOVE in the command line. Followed by the start coordinate 32000000,0 and the target coordinate 0,0 (for zone 32). After the export it won't have the zone number included in the X coordinates because of the artificial move.