Half-Life: Source sort of works like an expansion to Half-Life 2, which is why it installs into the Half-Life 2 folder, as well as some of Half-Life 2's files for it to be able to run, similar to Opposing Force and Blue Shift with the original Half-Life.

I'm no Source Engine expert, but I think some technical things changed within Half-Life 2 in the 20th Anniversary update, and Valve didn't update Half-Life: Source to work with the changes, so it breaks.

Half-Life: Source installs the 20th Anniversary Half-Life 2 files alongside it, and you can't revert to the Pre-Anniversary ones within the properties of Half-Life: Source because build changes only apply to Half-Life: Source itself, so this game is literally unplayable unless you install Half-Life 2.