A website says my safari browser is out of date but the Apple store doesn't have any available dates for my MAC

Please refer to this excerpt from Update to the latest version of Safari - Apple Support:

If a website says that your browser is out of date

If a website says that Safari is out of date even though you're already using the latest version of macOS or the latest version of iOS or iPadOS, there could be an issue with the website. If you’re sure that you want to use the website, contact the website owner or developer.

Safari updates happen with OS updates. It looks like you may be on High Sierra OS and the site requires Mojave or later version of Safari to work. This is most likely due to security improvements offered by the later OS updates and probably only affects banking or tax refund sites.

I would recommend updating to the latest OS your computer will allow. This will give you the most secure system as well as the latest version of Safari. Some people wait a week or 2 after a new software version to let others discover any bugs first. This is understandable, but I just set it for automatic updates and try to embrace the changes.

For your specific site you are having trouble with, it should give the minimum OS requirements.