The public inbox relays should receive your notes if you are tagged on them. So all your replies, likes, zaps etc go to your inbox as well. New notes shouldn't. Because a reply cites a post, that goes also goes to your inbox/outbox to make sure your follows can find it when loading replies from you.
Short polling in the background + notifications for DMs incoming from private / auth enabled relays. Other than not trying to write all of my notes to the inbox and DM relays, as mentioned by nostr:nprofile1qqsw9n8heusyq0el9f99tveg7r0rhcu9tznatuekxt764m78ymqu36cpzdmhxue69uhhwmm59e6hg7r09ehkuef0qy2hwumn8ghj7enjv4h8xtn4w3ux7tn0dejj7qg4waehxw309aex2mrp0yh82arcduhx7mn99ueat4s3, this is the single quality-of-life improvement still missing for me.
As for longer-term features, I would vote for having a build with an embedded, pre-configured "native" Android relay, à la Citrine, exposed to the Internet with a public reachable onion address and pre-configured with sensible filters so that every Amethyst client also becomes a self-sufficient personal relay out of the box. This would be the dream.
Discussion
Got it. I think that currently new notes might be going to both the Inbox and DM relays. Also, I may be wrong, but I believe that aside from notes I'm tagged in and my own activities (self-replies, likes, zaps), Amethyst is also trying to write the original notes I'm interacting with, as well as various other types of notes, to the Inbox and DM relays. Here's what I mean:
