My EOL Pebble doesn't use any servers at all, with Gadgetbridge. Why should moving data from my watch to my phone, over bluetooth, require a server on the internet? Silliness.
An app store, watch face store, dictation, weather. those features are the reason it requires a server. That's what you give up by not using rebble or similar services.
Also, any third party apps that create timeline pins unfortunately need to go through a server.
You can sideload Pebble apps AFAIR. I vaguely recall doing that recently to restore the watchface on my wife's Pebble after migrating it to a new phone.
You can. It's nice to have a working app store though!