Just take out the battery of any phone like a fairphone and most will work.

If you're somewhat technically inclined, maybe the extra pins on the battery contacts are for NTC thermisters?

Perhaps attach a fixed resistor in its place to fool the phone?

The Samsung phones up to S5 did when I had them

Ive often wondered this too. A tablet with no battery would make a good Lyrion client.

Pixel has bypass power. It's unfortunate that it's paying Google. I've been very happy with my used 8 on Graphene.

Have you tried removing the battery out? I assume you did, but have you tried taking it to a repair shop and ask to short the charging pin to the battery power pin?

I think, either the LG p990 or the galaxy alpha, do work without battery

Some gaming phones have passthrough

Note quite what you're use case is, but if you're looking to have something permanently plugged-in without risk (or, at least microscopic risk) of battery swelling/fire, recent models of Samsung phones+tablets have a "Maximum battery protection" mode where you can limit charging to 80%. I use an old Galaxy S22 as a control panel for the solar+inverter+security systems in my travel trailer - its permanently plugged in and just happily hangs on the wall keeping cool and doing its thing.

I think most phones work with a battery removed. I think your best bet would be phones with removable batteries.

If I remember correctly, some of the ROG phones could actually run directly from the cable bypassing the battery. I think the idea was that it could be plugged in and gaming without wearing down the battery.