Hello bobseg2,
Since Safari is an integrated part of macOS, you'll need to determine if your Mac is capable of upgrading to a newer version of macOS.
Depending on your model, you can use the applicable resource below to see if your Mac supports a version newer than macOS Catalina 10.15:
Identify your MacBook model - Apple Support
Identify your MacBook Air model - Apple Support
Identify your MacBook Pro model - Apple Support
Identify your iMac model - Apple Support
Identify your Mac mini model - Apple Support
Identify your Mac Pro model - Apple Support
If your Mac is compatible with a newer version of macOS, the steps from this resource can help with getting it upgraded: How to download and install macOS - Apple Support
Should you continue to get that prompt, or if your Mac isn't compatible with a newer version of macOS, you'll want to reach out to the developer of that website. They'd be in the best position to help further with their browser requirements.
Take care.