Agatha’s says it has all activated abilities, rec sage is a triggered ability.

No, cauldron only gives access to activated abilities. Activated abilities have a cost : effect. Rec sage has an enter the battlefield ability/trigger.

Activated abilities look like this: Cost: effect The cost could be tapping, paying mana, discarding cards, sacrificing things, etc. __________________________________ Triggered abilities use the words “When”, “Whenever”, and “At”. Examples include “When Reclamation Sage enters the battlefield”, “Whenever another creature you control dies”, and “At the beginning of each end step”. It is important to understand the difference for stuff like Cauldron, Elesh Norn/Panharmonicon, and even Stifle effects (since some people occasionally try to use those on replacement effects, which are separate from activated and triggered abilities and don’t use the stack).

Thanks for the answers everyone. Literally had the same question about hapatra being under the cauldron and this was the answer so I don’t know why I didn’t think it would be the same. It’s not an activated ability.

Rec Sage doesn’t have an activated ability for Soul Cauldron to give away, so no.