In the imperfect world there is no perfect solution sadly!
Consider this mind wanderings from old guy who spent far too much time answering questions about Time Capsules and Time Machine.
I had read about Synology and did see something from ASUS at MicroCenter.
Going back to Tricker's post since it is his thread.
I don't consider a drive attached to a Mac thunderbolt port a viable solution
I'm also trying to keep it simple and "inexpensive"
I have both Synology router and Asus router and have tested Time Machine to both. (Note somewhat outdated but at least decent testing over longer period than any "REVIEW" which lasts a week)
Synology works very well. As far as backup is concerned I would put it tops in the router stakes.
I do have misgivings in Synology is a very bit player in Router space and they have built a grand total of 3 router models. The first one was not a success. The two current ones are getting older and no replacements have been announced. Note if you can pickup cheap second hand Synology RT1900AC they actually work fine for Time Machine backup. Wireless was poor so it is not a viable package for all in almost one replacement. However Synology keep the firmware up to date and it will work fine as a cheap Time Machine Network target.
Asus is excellent router.. IMHO the best of the domestic routers with continually updated firmware. It is far from flawless though, and concerning that Asus have not updated SMB protocol. You still need to turn on SMB1 for it to work. This is really a concern as that should have been deprecated long ago as both MS and Apple recognise it as source of malware (ransomware. )
I hit issues with Time Machine backups to the Asus which failed on a 2month cycle.. this is long before Catalina.. and I kept testing over a year.. with the end result I cannot recommend it at least in combo with Time Machine.
I do use Asus RT-AC88U now as main router and it works great in that role. I have restarted testing recently using Carbon Copy Cloner to USB drive. CCC is far more reliable cf TM. So far it has run only a couple of weeks.. so I consider that insufficient time for reliability testing. It is going well.
A number of other router manufacturers do include Time Machine compatibility. I saw very recent cheap TP-Link Archer C2300 has Time Machine extensions available. Netgear have long dabbled with it as have a number of others. The results are far from great even in reviews.. that is without long term testing. Frankly if Time Machine is a major factor in a router purchase I don't think anything but Synology RT2600AC (or old 1900AC) should be on anyones list.
Honestly, a cheap NAS, Synology make one and two disk introductory models, should be high on your list.
It is going to outlast any router.
It is built for the job.
It is much faster over the network.
It has easily accessible drives which can be upgraded, replaced and setup in raid to hold data even in event of disk failure.
Synology has superior firmware upgrade cycle. When Apple make their inevitable changes which break things.. as per Catalina and the current Time Capsule.. Synology will update firmware in timely way.
I also run Synology (almost) NAS. IMHO it is far superior in every way to using a router.
Given that routers often have a far more limited lifespan than you are used to with Apple Time Capsule.. (10 years is miraculous though).. you are going to be stuck when buying another router because the existing USB drive may well not work in current configuration and need wipe and restart backup.