No, the games just disappear from the shop and can no longer be bought via Steam. When you are already own them, you keep them. Third party seller might sometimes also still sell remaining Steam Key inventory and thus offer a way to activate a delisted game on Steam.

One area where content can disappear is music licenses, those often don't result in a complete delisting of the game, but just the music getting patched out of the game. In those cases, the music would be gone for everybody, as Steam game updates are mandatory and you can't downgrade the game to a previous version either. Unofficial mods will sometimes address this issue and add the music back in.

No these games still install and run via steam just fine.

The are delisted for purchase but still available to download from Steam’s CDN for the Steam client. I own 3 delisted Transformers games but was able to reinstall them recently.

Tangentially related but even though the Nintendo 3DS e-shop has been shutdown for years you can still download your purchased games through your download history.

I was very happy just last week I was able to redownload Monster Hunter 3 Ultimate for my 3DS despite the store being down.

It gives me at least a little bit of confidence that having some games as part of a digital library on the Switch and Switch 2 will be easily available for the foreseeable future.