There hasn't been too much discussion about this, but the first point is to narrow down exactly what functionality would be desired on mobile.
A while back someone (I think it was @meeDamian ?) added push notification functionality for coinjoins from makers; that would be basically trivial.
Then you could go further and have like a control panel for remote access on phone, and still have same basic joinmarket on home machine. To go even further (1/2)
... and embed the wallet into the phone would be a substantial step up in work, and to not require an external jmdaemon, ie 100% on phone, even more (whole can of worms including Tor).
(jmdaemon was something i added in the rewrite in 2016/17; you can have the communications with peers entirely separated from the wallet, and the two talk to each over over TLS. At least one user actually does this)
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