I'll list almost all of the options with highest to least priority.

Necessities:

• Remove comment (with reason), and restore
• Remove post (with reason), and restore
• Lock post, and unlock
• View reports from users on posts and comments (I mean this) - This is probably the hardest to implement but it's also kind of the most important tool for moderators
• Ban user from community, and unban

These options are not as important to be present on the app but would still be very nice to have:

• View modlog of a community - It doesn't have to be perfect, just something to quickly see what's going on. This is something anyone can see!
• Feature/pin a post, and unfeature
• Ability to edit the community name and sidebar/About section, so you can make quick changes when needed
• Ability to see these stats (maybe in the About section), so you can see how a community is doing. Anyone can also see these stats too!
• Appoint user as mod, and remove them as a mod - On the desktop website, you should go to the specific user's post or comment on your community and select 'Appoint as mod' from the options to make them a moderator, which is kind of confusing if you don't know where to look. Hopefully there's an easier way to do this, where you can bypass that post or comment to appoint or remove any user as a mod (if possible)