I have the same experience and I once found a GitHub issue about it. I don’t think it sounded like they planned to fix it anytime soon. I just added the Tailscale toggle button to my phone’s quick control panel and turn it on whenever I want to check all my syncthing nodes or something. I keep meaning to see if I can script up something with Shortcuts to make it turn back off automatically.

Were you using an exit node? Because that really does hammer the battery, but vanilla TS without a bunch of traffic doesn't seem to do much to mine.

The only always-on TS service on my phone is Immich for photo backup, and I don't take enough photos for that to matter much.

Strange, battery use is negligible on Android, particularly when the tunnel is not in active use.