Yeah a lot of new devices can do it. Most new Samsung phones and tablets. There's a full list here

https://www.androidauthority.com/phones-with-bypass-charging-support-3509066/

I remember older ones doing that, the ones where you could hot swap the battery without turning it off. Nowadays no idea though.

I dont know of any specific ones, but in my experience, I haven't had one that wouldn't, as long as the charger could match the voltage the device needs.

i have many older (~2014) androids with replacable batteries and none of them can do it. however you can directly attach power to the battery connector to boot the device without a battery

As in android auto plug ins?

Nothing recent, but I know for sure that my old Samsung Galaxy S5 would run from USB power without the battery in it. It's trivially easy to verify, since the battery in that one was removable. Not many modern devices have removable batteries anymore, so that's going to be tough for people to test in a timely manner...

Basically any phone with a removable battery that i habe can do this. (Example, aus zenfone 2laser, fairphone 2, Galaxy note 4 was able to usw recovery., note 1, S7, also LG l70, Samsung s4 minj, Sony erricson irgendwas and Sony Ericson xperia irgendwas, shift phones. Ohh wait, none of what i said is true.m most of the could only be ised in recovery vor fastboot but i believe the zenfone 2 laser and the L70 Werke fully funktional.