Move selection after using the move tool (V) and then returning to the selection (M)?

I seem to work that way in all  version of Photoshop. If you switch from the move tool after moving a select area then switch to the lasso tool or marque tool and try to move the current active selection you will find that Move was not committed and the area you were moving moves with the active selection the content was not  merged into the layer. If you you make  an additional selection  by  using the shift  and add and additional area  to the active selection the move will be committed  and you will be able to move the active selection.  I tested PS 2020 and CS6 they work just like  PS 2021.  Photoshop delays committing some operations like transform  and move till you do something else. If   Photoshop committed  operation  like transform and moves while you were using the tool your document would be repeatedly resampled and degrades   the move would smeared along the move path.  Photoshop waits the you have finished using to tool to make a single move or transform, you final position and  transform.  Photoshop waits till it knows your done with the tool. When you do something else. Switching tools does nothing.  Photoshop does not see that as doing some other operation. Add to to the selection is something else. A shift click drag in some area outside the active selection. So Photoshop commits the move. dragging inside the active selection continues the move operation the has not been committed.

all the tools in Ps have keyboard modifier shortcuts and it's a good idea to always check and see how those work and what they do. In this case, make the selection, then hold cmd or alt to cut the image out and move it, then release. But the selection will not move after because that's not how the tool works. You created a type of layer and the selection is actively moving those pixels.