Airtags and similar can work, but there are downsides. For one, AirTags specifically have a series of anti-stalker features. That means a thief knows the bike is being tracked. Second, any tracker you hide on the bike can be found by a thief and removed.

Having it integrated by the manufacturer means both avoiding Apple's measures and making it much harder to find and remove. So it's generally a preferable option when possible.

I think it would be hard to hide an airtag effectively on a metal-framed bike. Putting it in the frame would interfere with wireless communication and any other location would be easily discovered.

That's correct [1], but there are plenty of accessories to hide one pretty well still.

[1] https://www.youtube.com/watch?v=aLtWN1Mp2Qc