Updating Unity means losing compatibility old projects?

I have Unity for a few years now, i noticed something. I made some of the tutorials, for instance Rogue2D. This game for instance i finished and was working fine in the Unity2018 version.

Now i downloaded unity version 2019, and it asks me if i want to upgrade to a newer version. I can only choose "Yes" or "Cancel". I would like to choose "No", because i don't want to change/convert my old projects, because they were working fine in te old version of Unity. So i choose "yes" and then my projects stop working, because a lot of coding mistakes.

How do i keep my old projects working after a major Unity Update? I dont want (and i can't) manually change all the codes. For instance one update suggests: "For all those methods you will need to add manually using UnityEngine.Animations; to your script" I only update Unity once a year, so maybe i missed twenty or more of these kind of updates i have to update manually. Thats a lot of work for a game you finished earlier on, and annoying because no idea if i can fix all the bugs. Any tips how to update? Or do i have to keep the old version of Unity also on my computer so i can still work or reuse parts of older projects?