I run a Piped instance on a VPS for myself. It's not linked to my Google account or my home IP (from Alphabet's perspective) in any way. I like giving Alphabet less info about my behavior.
YouTube will make recommendations based on your immediate session's viewing history, even without an account.
A tremendous advantage to viewing without authenticating is that you can quickly set a strong affinity based on your current interests, and don't have to live with consequences of viewing low-quality content for hours, days, months, years, millennia, etc.
If Invidious and Piped offer(ed) the option to permabam channels as well (to those subscribing directly to those services, or even within a single session), so much the better.
I hope you don't mind me asking for info, but how beefy is the vps? I can't find minimum specs for these frontends, and that would help me know if I have enough spare power at home. I imagine you want all the bandwidth you can get, but are there cpu limitations?
Everything put together appears to be using 368 + 94 + 16 + 37 = 515MB of RAM while watching a video. I imagine you'd want some overhead (the backend is mostly Java) and this doesn't include the reverse proxy. Seems to use fairly low amounts of CPU. (My VPS is 5 Epyc cores and 9GB of RAM, so way beyond what it needs for this.)
Doesn't that still leave YouTube with one unique IP address that all your traffic is originating from? It would in any case close off some tracking vectors if you also use other Google products from your home IP address but I guess you would also need a proxy/VPN or share the instance to get any kind of anonymity.