Personally, i would use VPN, Pihole for Local-DNS Records and a simple Local Reverse Proxy to address my Network-Services. I wouldnt open anything from my Homelab to the Internet.

No Problem :)

I think there is an APP for all major Plattforms (Desktop and Mobile):

https://stoat.chat/download

iOS and Android are listed.

Or what do you mean with mobile client?

Maybe Stoat/Revolt is for you. Stoat has - in my opinion - the same look and feel as discord.

It is OpenSource, selfhostable and it comes with most features discord has - excluding nitro.

There is an Android, Linux and Windows APP.