1 Some of what you have done on the network matters.
Catalina is definitely an issue. Loads of people are having issues with it.
3 Your Time Capsule maybe suffering old age.
That can affect a number of things.
But the chief one is this..
2 I moved homes and therefore internet setups (although with the same ISP). After testing and finding the wifi connection with the new ISP-router to be better than the Airport, I no longer use the Airport as my router (as I've done for years). I disabled it as the router by switching it to bridge mode.
There is a ratio of speed used by LAN and WAN. Lets say the old connection to the TC in previous house you had 20Mbps internet speed and a true network throughput on local LAN of 300Mbps. When you backup you will average about 200Mbps in the backup, and still have full 20Mbps for internet access.
Lets say in the new house you have lower throughput due to greater distance.. So 150Mbps which is plenty for your internet. You will not notice any great slow down between your two houses.. but when the backup starts and it fully saturating your 150Mbps then you have no more capacity for internet..
Plus a different router is now controlling the connection. WMM which is QoS for wireless.. something you never saw in your TC setup but was there.. controlled internet giving more priority to internet than bulk backup which should be low priority.
This is just one scenario.. I can make up as many fictions as average Star Wars novelist.
What you need to do is put hard number to setup..
So I need you to do a few tests and report the results
1 What is your link speed to the Router?
You can do this with holding down the Option key.. click the wireless fan and check the link.

The screenshot helps me to see.
2 Ookla speedtest to a close ISP to get your best internet speed. Post the details.
3 With internet not running.. just disconnect in the main router from your WAN.
Run a backup to the TC and give me average speed.
Activity monitor on the Network tab will give you a good idea.

Now I also suggest you do a couple of simple file transfers to the TC in Finder.
I use 6 video file of 1GB, you want large files to max out the transfer speed rather than measuring how poor the disk in the TC is.. it is pretty poor.
You should get something like this.

It does bounce up and down a fair bit but you can time it and calculate the average or do engineers aprox with picking the speed that is around average.. in my case around 22MByte/s
It might also be worth looking in activity monitor at free memory and processor usage.. things go wrong and it can be processor issues due to something not envisaged.
Pass me all that info and I can work away at what is happening.