For me, it didn't prompt the upgrade when I went to the firmware page, but it did prompt for it when I went into the matter settings page.
I think Switchbot does slow rollouts, but if it's not available for you yet you can just send them a message in the feedback page of the app and they'll probably be able push the upgrade to you (I've done this a couple of times for previous matter releases).
To provide a counterpoint, I think it can definitely be worth it to throw together a cheap VR setup for this game.
I personally went through Half-life Alyx on my original Oculus Rift CV1 and it was still an amazing experience. I don't know where you live, but in my market a good condition CV1 is selling for about 10,000 yen (so that's equivalent to 65 USD, but your market will probably vary).
This is PC VR though, so you'll probably want a PC with at least a 1080-class GPU. Once you have the headset though there's a few games from the same era which had simlarly incredible experiences like Lone Echo.