Which free VPN tiers are usable, and which ones are quietly selling me? VPN

Worth checking whether you need a VPN at all here. Encrypted DNS plus HTTPS already hides most of what you are worried about from the router owner, and a lot of routers show only IP addresses in their logs anyway. Turn on encrypted DNS in your browser first, see what is left, then decide.

The one free tier I am comfortable recommending is Proton's, because it is funded by paid subscribers rather than by advertising, and it does not cap your data. The trade-offs are explicit: one device at a time, a restricted set of countries you cannot pick from freely, no peer-to-peer, and none of the extras. For "my landlord should not see which services I use on a network he controls", that is genuinely sufficient.

If your university provides one, use that instead. Mine had an institutional tunnel that was faster than anything I could have bought, and the threat model of a university IT department versus a landlord with router admin is a comparison most students never think to make.

Rule of thumb that has never failed me: if a free VPN advertises on video platforms, it is not free. The infrastructure cost of carrying your traffic is real and somebody pays it, so ask what they sell. Several of the store-front free apps have been caught injecting or logging over the years, and the permission requests you noticed are exactly the smell you should trust.

Do not self-host on a cheap virtual server to save money unless you understand that you become the only user of that address. It is great for bypassing a nosy network and terrible for blending in, which is the opposite of what most people want when they say privacy.