Time Machine backup very slow

Make sure that you are not running any kind of anti-virus application on your Mac, or any other type of utility that claims to "speed up", "optimize", "keep" etc your Mac.

Often, a first backup will run OK, but subsequent incremental backups take forever because the A/V application tries to compare everything on the Mac with everything in the back up.

Should I connect the Mac mini to the router via Ethernet or would it be possible to connect it directly to the TC?

Whichever is closer. It really makes no difference. I guess slight preference to plugging directly to the TC.

I copied a 2GB movie file to the Data folder on the TC. Took around 10 minutes, speed in the activity monitor was between 6 and 10 MB/s.

That pretty much proves the network is not the main issue. And agrees with your first backup being fairly fast. While your speeds are not fantastic it is good enough to copy 2GB in 10min Time Machine moving 1.4GB is taking so incredibly long I am thinking issue is more along the lines of TM.

Still worth trying ethernet as TM is doing a lot of other things in the background and 2 way communications over ethernet is hugely faster than wifi.

Are you manually backing up once a day rather than leaving TM to manage it as normal on hourly schedule?

1.4GB is big for an incremental.

Outlook data files to be difficult for TM

Time Machine is copying the file.. and it should not have any more issues than any other file. It is likely big.. but since you have only 1.4GB total for the backup that is not ridiculous yet. It may actually be worthwhile excluding the MS Office files and see if that gives you a speedy backup.

Going back to the start you said ...

I have already deleted the TC and started from scratch

Just to get this clear.. you did erase the TC from the airport utility? Everything is removed when you do this.

If you just deleted the backup via Finder that is not good enough with Big Sur .. you need to erase the TC. And then backup the Big Sur computer first. This is important as it allows a major change in the backup from old to new Mac format.

It will delete the backup from your other computer so if you need to keep that.. archive the TC to USB drive first.

My other recommendation is to try Carbon Copy Cloner. It is free to use for a month and does a much faster and more reliable backup of your computer than TM. If there is enough space on the TC you can try it without the erase I mentioned.

You will need to create a sparse bundle on the TC for CCC but you can create it in a separate folder. It is fairly straight forward to configure with lots of help included.

WiFi can be very difficult.. and I don't see why the initial backup is fine but incremental so slow.

What actual speed are you getting via wireless to the TC if you copy a single very large file directly to the disk in Finder.

You can use activity monitor to get an aprox. speed.

What model is the TC and how old?

Is it setup as your main network router or in bridge to another router?

Can you test with ethernet instead turning off wireless.. even just as a test, it will show if the issue is the TC itself or wifi problems.

I agree with LaPastenague that it would be worthwhile to temporary set up Time Machine to "Exclude" the Microsoft files from backups to see if that might make any difference in the duration of incremental backups.