I compiled a list of reducers I should update by searching for existing reducers of PROCESS_MESSAGES and PROCESS_UPDATES. The former is only reduced in message-reducer.js, while the latter is reduced in all of the below reducers.

I excluded three reducers that currently reduce PROCESS_UPDATES:

1. reduceKeyserverStore, which keeps track of updatesCurrentAsOf for keyserver updates. We're using a different mechanism to verify and track DM ops.
2. reduceCurrentUserInfo, which should not be possible to affect with DM ops.
3. reduceUserInfos, which should not be possible to affect with DM ops. The UserInfosHandler should handle populating the UserStore when new users are encountered via DM ops. Tracking this in a new task: ENG-8829.

Submitting this now so @tomek can see the code, as his work relates to this code.

Depends on D12780

Test plan described here