If you allow for servers that can't read your messages (Tor nodes and such), "serverless" messaging is quite possible. All the layers of encryption and redirection aren't great for latency, but there's no reason two phones can't be connected over Tor/Veilid.
The problem in practice, I think, is notifications. To receive notifications, you need to be online all the time. To be available on Tor all the time may help deanonimze you so you also need to shake up your connections every now and then, which requires some CPU heavy recalculations and key exchange from the network as connections are reestablished.
Not exactly what you're looking for, BUT the best bet would probably be jabber/xmpp. There is a server involved but you can be that server with a ras pi or an old laptop, or VPS, and with OMEMO e2ee, the server can't see message content only "bob sends X to john." And as the server owner you can keep no logs and trust yourself.
simplex uses relays/servers, but incoming and outgoing messages are configured to pass through separate servers. you can see this in the network settings
Session doesn't store logs on a central server. They are encrypted and stored on lokinet.
Anyway other options are: Jami, Signal or Molly and maybe matrix. Keep in mind Briar will drain battery a bit and doesn't receive notifications offline unless you setup a dedicated device
session tries to promote their oxen cryptocurrency and lokinet which imo crypto currency are used by baiters to bait people into ruining their money
you dont understand what signal /molly is , do you ? they are centralized server and OP specificially asked not centralized server / server for that matter
matrix is good but it still need server , plus matrix.org takes quite a bit of metadata
jami's good but it uses turn server to verify your name
briar's bluetooth functionality can be violated plus no good ui/ux
it's very well thought out ! The features make sense.
UNFORTUNATELY it's not P2P ! all the messages pass by their servers :'( with Briar it's P2P....
weirdly they claim their way is better than P2P ! any comment on that ?
In my point of view, if messages are stored somewhere it's mean the can be process[^1] !
Direct peer-to-peer connections giveaway your IP address to the person you're communicating with. Meaning anybody observing the network can see two people are specifically communicating with each other. Briar attempts to get around this by using Tor to obscure it.
But briar is using Tor as a relay, just like simple x does. The architectures are very similar from that lens.
To your threat model, ideally data does not rest on the network, but you have to assume any data that hits the network is being recorded by a bad actor to be analyzed later.
It's been stuck in "coming soon" hell for ages, but VeilidChat may be of interest to you.
TorChat is rather clunky, but any privacy respecting chat app without an intermediate server will be. Is a bit like Tor but with some improvements, so running a chat protocol on top of it should work better.
Note that there is an app called "veilid chat" out there that doesn't seem to have anything to do with the people writing code on the Veilid network.