Does anyone know someone who actually has received the six-digit code on their phone using this EU Exit: ID Document Check app? Or is it just not working for anyone?
(intentionally not working possibly.. it's about settled and pre-settled status)

It works just fine.

It does not, the text with the code is often not sent (to me the word is never), there are loads of references about this issue online.

Five million successful applicants say otherwise.

Wow that's a lot. Didn't know. Still, the app has a 1.4 rating in the app store, so can't be all fun and games.

Are you based outside the UK? Your service provider may be blocking the text message.

That would not be my case as I receive texts from all over the world for work.

It could be down to network not supporting code format, try different sim card from one of big names.
You can try pay as you go sim card, can be ordered online for free.
Also, you can try this: Message - Support - Three) .