Tahoe Private Relay - websites know my city?

If you went to that website before you used Private Relay they could have added a cookie that may show additional location data to be used when you access that website again. Also if you signed into a website where you created an account, they have the information that you gave them when the account was created.

With Private Relay, you have 2 options for how specific you want your location to be known where neither of them are your exact location. If the website just knows your City, I suspect you have yours set to Maintain General Location. That means if you search for a business in Safari, you are more likely to get relevant results locally.

Go to Settings > [your name] > iCloud > Private Relay > IP Address Location, then choose one of the following:

• Maintain General Location (for example, to see local content in Safari)
• Use Country and Time Zone (to make your location more obscure)

Protect your web browsing with iCloud Private Relay on iPhone - Apple Support (IN)

I think using a VPN can be problematic.

The only time I have used one was with an employer-provided VPN custom configured for the corporate network for remote use only, to protect proprietary information and to meet government-mandated security requirements of contractors.

Ordinary over the counter commercial VPNs have proven to be security risks in the past. A commercial VPN is like paying someone to carry your paper mail from the mailbox to your residence and along the way they open and read all your private paper mail before leaving it at your home. Would you trust such an arrangement. VPNs are like an electronic version of that. Many VPN companies have been embroiled in scandals or breeches or even lawsuits for violating the customers' trust.

A VPN can sell your information to whomever it wants. So maybe it is passing that private information on to third parties, we just don't know, but this sort of misbehavior has been uncovered in the past.