Genuine 'Network Provider Settings Update' prompt on iPhone?

You ARE well-served by NOT clicking on anything unknown, arriving unexpectedly, and of unknown origin. 👏👏👏

However, carriers DO send updates.

I’d suggest following this procedure to provide a somewhat higher level of assurance that any update is legitimately from your carrier:

Manually update your carrier settings on your iPhone or iPad - Apple Support

That said, IMO carriers could indeed do a much better job in this regard.

What happens if you tap Settings > General > About?

Is there anything like a message or notification there about a carrier update?

Reference: Manually update your carrier settings on your iPhone or iPad - Apple Support

is it genuine? (And how do I know?)

Did you contact customer support at your provider and ask them if they have issued a new update?

Re: “…They should have this information on their website …”

I think we all agree that they should. (at least for authenticated subscribers)

My own carrier does NOT make this info available online. (Telcos are traditionally - and for some very valid reasons - VERY tight-lipped about their engineering)

And most of us would probably rather have a tooth drilled than speak to a carrier’s Tier-1 CSR after an extended “hold.” 😩

I too considered suggesting this, but have lingering doubts if the Tier-1 CSRs would even know about it …

… potentially leaving the subscriber w/ a false impression as to the genuineness of a legitimate change.