There is actually a Chinese solution to this which you wouldn't prefer at all. Legally every place who provide free wifi will need you to do sms verification with your smartphone, and record your ip with your smartphone number (which in China is connected to your identity). Then they need not worry about liability, because if anything goes wrong, they can tell the police exactly who you are.
If you want both privacy and liability, it seems indeed only you can do is to be harsh on larger entities like cafe shops who provide free wifi.
Actually you cannot use your present Mullvad account to do so. Instead, Mullvad provided exclusive API for tailscale as partner account to do so, which you can only get from Tailsacle if you choose their service. Mullvad only allows those data to go through its server.
Given that Tailscale is a ridiculous company that advertises on privacy while force user to login via SSO by tech giants or OIDC which is shit in privacy, I will stick to my current origin Mullvad account and keep away from this service.
It is really fascinating that the first website I went to is exactly named "Why bkuhn's Website Looks Like Crap", where someone explains why he is sticking to Web 1.0.
If you want both privacy and liability, it seems indeed only you can do is to be harsh on larger entities like cafe shops who provide free wifi.