I can't reproduce the issue with my "working" profile with QGIS 3.40.4, but strangely it occurs with a new profile

@mblesius, thanks for testing!
If, using your "working" profile, the new layer shows a valid CRS assigned to it when it is subsequently loaded in QGIS after the creation, then that is due to the fact that you have set an option different than "Leave as an unknown (take no action)" - which is the default - in Settings -> Options -> CRS and Transforms -> CRS Handling -> CRS for Layers. Could you check, please? How are set such options? What is the CRS of the layer as displayed in QGIS? May please check the actual CRS of the layer using the "Vector information" GDAL processing algorithm with the "Enable listing of all layers in the dataset" option set?

Yes, you're right. I've set this option to use the default layer CRS which is EPSG:25832 in my case. I didn't notice the warning message at first. Thus, I confused UTM Zone 33 for Zone 32.

Same with Layer > Save As... for a layer that has no CRS set.
The CRS selector in QgsVectorLayerSaveAsDialog is used to reproject the data, not to be assigned to the data.

This looks like expected behavior, since the transformation from invalid crs fails, though we probably could communicate this better to the user.

@uclaros, looking at the code, it seems to me that such case (invalid source layer's CRS) was not taken in consideration, since in such case an invalid Coordinate Transorm is unawares created (while the invalid destination layer's CRS case was considered, and in such case the Coordinate Transorm is not created), so I think such behaviour is not by design. I'll propose a PR to fix it: it is reasonable to me that, in such case, the chosen CRS should be assigned to the new vector layer.
I think the CRS selector in QgsVectorLayerSaveAsDialog is used to set the CRS of the output layer and to reproject the data if needed.
The "Vector General - Reproject layer" processing algorithm creates an output layer with a chosen CRS even if the input layer's CRS is invalid (without obviously performing any reprojection).

I think the CRS selector in QgsVectorLayerSaveAsDialog is used to set the CRS of the output layer and to reproject the data if needed.

Both the code and the documentation suggests that this CRS is for reprojection, not assignment. I think it's more appropriate to disable the crs selector and show a tooltip if the source crs is not valid. Let the user fix his layer, then try again.

The "Vector General - Reproject layer" processing algorithm creates an output layer with a chosen CRS even if the input layer's CRS is invalid (without obviously performing any reprojection).

I'd consider this a bug as users would expect the coords to be reprojected as the algorithm name hints, not just transferred unchanged!

@uclaros, in the meantime I've found another glitch in the Paste Features As functionality:

1. new project with the World Map layer
2. copy the text

wkt_geom fid
Polygon ((602049.70009776263032109 4531463.99115845467895269, 621551.28105399641208351 4540522.10253156814724207, 619526.52674706501420587 4524643.76612458005547523, 604607.28448546538129449 4521127.08759148884564638, 602049.70009776263032109 4531463.99115845467895269)) 1

3. Edit -> Paste Features As -> New Vector Layer -> the dialog window shows CRS Invalid, which is correct. Close the dialog window
4. select a feature from the World Map layer and then Edit -> Copy Features
5. Edit -> Paste Features As -> New Vector Layer -> the dialog window shows CRS EPSG:4326 - WGS 84, which is correct. Close the dialog window
6. copy again the text from point 2.
7. Edit -> Paste Features As -> New Vector Layer -> the dialog window shows CRS EPSG:4326 - WGS 84, which is wrong