I'm confused about which items can be transformed via the Catalyst

I didn't understand how it worked back in Dragonflight Season 4, and I'm still confused this season. I'm trying to step up my gameplay by doing raids and Mythic+, but I'm unsure which items can be transformed using the Catalyst.

For example, I have a 584 ilvl shoulder piece that I got from renown, and I was able to transform that. However, I can't transform my 587 ilvl heroic dungeon or world quest gear (I know crafted gear can't be transformed). So, what items are eligible for transformation? Can I transform Mythic+ gear? Does M0 gear count? How do I know which appearance the item will transform into (normal, heroic, or mythic)?

Also, is there an addon, website, or in-game menu I can use to check which dungeons or raids drop certain item levels?

I appreciate any help you can provide. Just trying to improve and understand the game better!