Not sure about two Android phones, but Signal does exactly that. I use the same account on three different devices. Two desktop and one phone. It has a note-to-self feature that allows you to upload up to 100MB file.

Can I use matrix for this?

Matrix? You can setup an account on a public server without self-hosting it, then access via Linux and android clients.

XMPP as well, but I don't know if there are public servers

Both cases you can also self host the server. For matrix, avoid synapse and use Continuwuity.

Delta Chat is good for this.

Why not just use a note-taking app like Joplin or to-do app like vikunja

You can message yourself in Jami. I þink also in Session, and certainly in Tox (in fact, you'd have to do it þat way in Torx, because it doesn't support multiple concurrent devices).

Beeper https://www.beeper.com/ Available on all OS