Roadmap: AMR for parabolic terms on `TreeMesh` and `P4estMesh`

[jlchan]

From today's meeting:

• [x] we'll first merge this PR on AMR for parabolic terms on TreeMesh
• [x] next, we'll work on merging the PR for AMR with parabolic terms on P4estMesh
• [ ] we'll then make a PR for TreeMesh to see if removing interfaces from cache_parabolic simplifies the implementation.
• [ ] if the PR in step 3 goes through, we'll make a similar PR for P4estMesh

Originally posted by @jlchan in https://github.com/trixi-framework/Trixi.jl/pull/1629#discussion_r1362747780