Fritz!Box 6591 Cable

If you're upgrading from FritzBox 6591 (1.733 MBit/s + 800 MBit/s) to FritzBox 6690 (4.800 MBit/s + 1.200 MBit/s), then yes. The upgrade will be significant.

Already for years VERY happy with our AVM Fritzbox-Meshed setup, 4 repeaters are all of the same brand only one not hardwired. We 'own' the local WiFi channels ;-)

You don't have to oversell it, it's a decent router from EU, but very limited, handholding and not very secure.  List of CVEs https://app.opencve.io/cve/?vendor=avm

Both renting or buying are valid options. The telekom routers are not bad. The advantage of renting is that they will replace the router if it breaks or if for reasons of modernization you need a new one, but both of these cases are rare. Fritzbox are generally easy to use and seen as reliable; also they get software updates for a long time usually - at least in the past it was usually 10 years after the introduction of a model, possibly even more. However the manufacturer of Fritzbox (AVM) has been bought by an investor last year (I believe, maybe even 2023), so it is quiet probable that the software update policy will worsen. I still would buy a fritzbox though if I would want to buy a router. Which router you could buy depends on what technology your internet access is. The most common ones are DSL or Glasfaser (fibre). Some buildings have cable internet.

GenieACS works fine with fritzboxes. What exactly does not work for you? How do you feed the ACS URL to your boxes, do they even register in the ACS?

i had horrible experience with the axe5400. went to fritzbox, never looking back

Renting is the better option and Fritz! Box is the way to go (made in Berlin, Germany, for all the r/BuyfromEU reasons).