AirPort Extreme replacement

You have posted your question on a user to user support forum..........we are all users here, just like you. No one from Apple is here, and no one from Apple will respond to your post.

Apple discontinued the AirPort router line in April 2018 so there are no replacements from Apple for these products. Currently, Apples does sell the Linksys, Netgear and Eero mesh systems online and in their stores, but they offer no support for these products.

Time Machine is available on a small selection of routers, of which the Synology RT2600AC is perhaps the best.

You need to plug in a USB3 drive for backup.

It will do a lot more than you are asking.. print serving and 4G fallback etc.

Other brands also include it but with some problems.. Asus is a brand I really like.. all their high end models support TM out of the box.. but I found it unreliable long term. YMMV.

Netgear, has some models that support it.. so do TP-Link. Neither company is likely to update firmware once a router is on the market as they don't sell firmware.. they sell routers. Support is after thought.

Or buy a NAS which is much more expensive but also far more flexible and will last much longer. You can plug it into any wireless router you like.