Facebook says my browser is outdated Ventura 13.5.1 some Facebook apps don't work.

Excerpted 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If a website says that Safari is out of date even though you're already using the latest version of macOS or the latest version of iOS or iPadOS, there could be an issue with the website.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.

How do you get the messenger me iOS app and for messenger-me? What does it do