So far nothing seems to indicate that it's happening. The question is if it's due to Apple's "measures" or just because it is not worthwhile for Meta/Alphabet. I think it's a combination of. But if it was as easy to "side-load" an app on iOS as on macOS - per your suggestion, I'm confident Meta would have done the switch in a heartbeat.
Just imagine if Apple provided nice API's for auto-updating, essentially no limitations on what binaries can be attested, API's/mechanisms for easy migration between AppStore apps and side loaded ones, no scary screens etc. Essentially implementing the DMA to the fullest extent, really honouring the intent of the law. Why wouldn't all the mega apps just move over? And what consequences would it have?
I think it would be awesome to e.g lift the JIT blocking and allow more strange niche things in alternative app stores. But getting all regular people on a wild-west third party app stores for the (ad financed) apps the use every day is just begging for a huge _actual_ loss in privacy.
[0]: https://en.wikipedia.org/wiki/Identifier_for_Advertisers#App...