Do I first have to backup apps I want to disable on iCloud?

I just switched to a new phone with a larger capacity, so installed more apps than the previous phone, then noticed that backing up to iCloud has been disabled due to lack of space.

I do not want to backup my online games (Genshin Impact, Honkai Star Rail, Tears of Themis, Wuthering Waves, and Zenless Zone Zero) since they're all server-based, but iCloud seems ****-bent on having me back up more than 200gb of that game file data before I can even disable them from iCloud. Is this really how this works?

Is there no way of disabling them from getting backed up BEFORE THEY GET BACKED UP? And yes, I find it wasteful to pay for iCloud+ just so I could initially back these apps up just to disable them from future backups.

Further, is there a way to disable backing up new apps (which btw, most apps run off of their own respective cloud services and require no app backups whatsoever anyway) from getting backed into iCloud?