You should be able to be clever, and make a copy of the installed older version, and remove the 'game' folder contents - and copy the 'game' folder contents of the new version into the copy you made - and it should work. Technically. :>)
Tried your method got this error meassge:
I'm sorry, but an uncaught exception occurred.
Before loading the script.
ValueError: unsupported pickle protocol: 5
-- Full Traceback ------------------------------------------------------------
Full traceback:
File "renpy/bootstrap.py", line 326, in bootstrap
renpy.main.main()
File "renpy/main.py", line 382, in main
renpy.loader.index_archives()
File "renpy/loader.py", line 244, in index_archives
index = handler.read_index(f)
File "renpy/loader.py", line 129, in read_index
index = loads(zlib.decompress(infile.read()))
ValueError: unsupported pickle protocol: 5
Windows-10-10.0.19041
Ren'Py 7.4.8.1895
Fri Aug 19 23:25:45 2022
Never heard of pickle protocol: 5