Outpost has an early Android app as of v0.2.21 — the same web client wrapped with Capacitor into a real installable app, rather than a browser tab. It's a debug build, not something distributed through the Play Store, so expect rough edges.
Grab the APK from the download page or directly from GitHub Releases. It isn't signed with a Play-Store-issued key, so Android will ask you to confirm installing from an unknown source the first time — that's expected, not a sign of a bad download.
Voice works end-to-end as of v0.2.21, including push-to-talk. Getting there took two real fixes only findable through testing on an actual device (a Pixel 6 Pro): the WebView wasn't forwarding the page's microphone permission request to Android's own runtime permission system at all, and once that was fixed, the microphone still couldn't open until the device's audio system was explicitly put into communication mode. Both are handled automatically now — you'll just see a normal "Allow Outpost to record audio?" prompt the first time you join a voice channel.