How do I send a fax with a fax modem (USR Model 5637) with OS/X Catalina?

No work around. OS X simply doesn't support analog modem connections any longer. There are no drivers available, period. Your choices include Fax apps that use the internet to send faxes. For most of those, however, there is a charge for sending each Fax. The other solution is an all-in-one printer/scanner/fax. I have the Epson WF-2860 and can send/receive faxes without issue on Catalina.

I don't know if you want to go to this extent, but you could attach an external drive, install an earlier OS on it and then use it as a start up drive when sending your faxes. I've done this in the past when there were older 32 bit apps I need to use on occasion. I also used the drive to back up all my files.

There are a number of on-line FAX services, but there are no solutions that I'm aware of that allow the use of external modems.

There are also many web-based Fax services that don't use modems.

Do you have an older Mac capable of running Snow Leopard thru Mavericks on it. That will have indigenous OSX fax support on it and should work with your USR modem.

Short of a dedicated FAX application from the Mac App Store, there is no restoring native FAX operating system support to your 16 in MacBook Pro.

That new 16 inch MBP will not boot external drives containing operating systems older than Catalina. Bump.

There are several FAX solutions (search for FAX) in the Mac App Store. Perhaps one of these also supports your USR modem.