How do I find out what VPN or other software is installed preventing me from using Private Relay?

Private Relay is not available in all countries and regions. From a press report quoting Apple back in 2021, the following countries and regions did not have support for Private Relay: China, Belarus, Colombia, Egypt, Kazakhstan, Saudi Arabia, South Africa, Turkmenistan, Uganda, and Philippines.

As for issues from first-few hops VPNs, remove those per the vendors’ instructions, and test again.

Look I n t he Applications folder. They're all there.

I would hope you knew what VPN you installed.

Sometimes, it is difficult to identify why it doesn't work. I have heard that reinstalling can sometimes fix it if you don't have anything else blocking it.

You can look in your Wi-Fi settings, Details, Proxies to see if there is anything there. Again, you should know you set that up.

I would imagine any ill-advised internet security software would cause issues with Private Relay.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Here's some food for thought: unless you're using a true VPN tunnel, such as between you and your employer's, school's or bank's servers, they provide false security from a privacy standpoint.  Read these two articles: Public VPN's are anything but private and Former Malware Distributor Kape Technologies Now Owns ExpressVPN, CyberGhost, Private Internet Access, Zenmate, and a Collection of VPN “Review” Websites.