They haven't moved it online. Find a TV and switch it on - BBC Four is still there, for now at least!

https://ukfree.tv/channels/all/Freeview

I've noticed this a lot with anti-BBC folks. They have some ideological issue with it but that isn't a popular position so they go for more niche arguments like "The entire historical catalogue isn't fully available to watch on demand" or "They axed BBC <insert number> from broadcast". Arguments they don't actually care about. It's just a way to snipe at the BBC.

As you've pointed out, if someone loves being able to watch BBC Four on broadcast TV, they're not going to be complaining about it's non existent axing.

I’m very pro BBC - but they reached their apogee in the early 2000s and have been in a state of steady decline since.

Yet you know nothing about it.

The problem is that BBC Four now only shows archive material (with occasional exceptions as "overflow capacity" from sports events etc.) whereas they used to commission their own documentaries.