Yes, you do. PSVR 2 is not backward-compatible with the PS4 and requires a PS5 to operate. It is not a standalone VR headset, unlike Meta's incredibly popular Oculus Quest 2 headset.
If you're yet to get a PS5 you might be able to get the two bundled together next year, but it's unlikely you'd save any money doing so. Plus, that would have you still waiting until February for a PS5, so we'd grab one now if you can find one. Especially as God of War Ragnarok is finally out.