Safari 14.0.2 User Agent defaults to old version for Safari 4.0.4 and can't be permanently changed

Safari chooses the incorrect User Agent for each new tab:

Mozilla/5.0 (Macintosh; U; Intel Mac OS X 10_5_8; en-us) AppleWebKit/531.21.8 (KHTML, like Gecko) Version/4.0.4 Safari/531.21.10 FBSMTWB

This generates the response "Your browser is not supported" when I try to open iCloud or use PayPay.

I can change to the current User Agent in the Develop/User Agent menu which fixes the problem but I have to do this for every new tab:

Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_6) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/14.0.2 Safari/605.1.15

I recently upgraded to Big Sur 11.1 and Safari 14.0.2 but I had the same problem before the upgrade, so re-installing macOS and Safari hasn't fixed it.

It's really frustrating that I can't set the default User Agent in Safari 14.0.2 to "Safari 14.0.2"!!