First off, I know you said no auto-high bids... this sentence alone should prove it's not an auto-high bid. Second, I wrote a mail app once called Prioritiz in Objective C, years ago. I wanted to use Chillkat but we used the free library to get started. Oauth wasn't implemented... although I did use Okta at my last job.
I put a higher time frame and bid because I know what it takes, and you're right, it's not "simple". Mail protocols behave funny. You can't download the "last 50" because the unique ID's not guaranteed... well you can, but if you get more than 50 emails between checks, you'd have to indirectly figure that out. Is that why the dude quit? Heh...
Anyway, deleting is also a pain. The protocol never deletes directly either, it changes status, then changes status again, THEN finally deletes.
I initially bid higher and extended the days... but then I reread your description, and it looks like just Swift custom UI tweaks and Oauth? If your previous dev wrote spaghetti... so long as the UI and data are decoupled, shouldn't be too big a pain. Before you ask, yes, I know Swift... 3, 4, and 5. Well, all technically, but those are the modern ones being used.
I'm unemployed currently, do driver gigs in the evening, and have a possible final interview in another state for a job. So I might be distracted, but can probably devote 7 hours at least a day for 7 days. I'm still nervous on matching the time-frame if there's more detail or spaghetti. Can message about it