I tried everything but nothing seems to work

Pretty sure this isn't an issue with this mod. Make sure your creature mob cap isn't full and your spawn area is in a good biome. Passive mobs try to spawn 400x less often than hostile mobs and their mobcap is 7 times smaller, so getting them to spawn needs knowledge of their spawn mechanics. Maybe test in a creative world.

I tried it in multiple Creative Worlds, multiple altitudes and bioms. I don't get it to work in the skyblock worlds

Hmm. I just created a new world in both 1.19-4.1.3 and 1.19.2-4.1.3, used /fill to create a grass platform and cows, sheep, chickens etc spawned immediately. What version of Minecraft and the mod are you on and how are you testing?

Well, I'm testing the same way with version 19.2-4.1.3 and the /fill command. But I now tested with just carpet mod and without the Add-on and it's not working either so it must be something with carpet. Ofc I tested it without any mods too and it worked...

After installing a older version of carpet it worked flawless.

Maybe submit an issue to the Carpet mod then. Thanks for reporting.