The Samsung Galaxy Note 10 Lite does that. If I’m not mistaken, some budget phones nowadays still do that.
Even if they don’t, as long as there’s a headphone jack, it might be possible to add good FM Radio support with NextRadio/Spirit2. You might need to root your phone, though.
That's probably true of all of them. Strictly-speaking, an FM radio with a telescoping antenna can pick things up without extending the antenna, but it's gonna do a pretty poor job.
Sure, but they usually lock you out in software. For example my phone (Poco X3 Pro) will let you turn on FM radio but not tune without antenna connected. Others usually don't let you use it at all.
I guess it's because people kept sending them reports of "FM radio not working".