I've got a "newish" 2019 16" MacBook Pro.........Got that.
I read I should do this via Migration Assistant..........If you read this, the information was not correct. Migration Assistant would be used only if you already had backups of a Mac......and......you wanted to transfer the data from a backup of an "old" Mac to a "new" Mac, so your new Mac would look just like your old Mac.
What am I doing wrong?........Trying to use Migration Assistant to back up the new Mac.
If you want to back up the data on the new Mac, the Mac must be on the same network as the Time Capsule.
Click to open System Preferences........the gear icon on the dock
Click to open Time Machine
Click Select Disk.....or it might say Add or Remove Disk.......and select the Time Capsule......named "Data" unless you have changed the name of the hard drive on the Time Capsule....... as the destination for backups from the new Mac
Click Use Disk
Wait for Time Machine to start a backup. You may see "Preparing" for a long time before the actual backup begins. Time Machine will copy everything on the Mac over to the Time Capsule, so the first backup is going to take some time.....4, 6, maybe 8 hours. Let the backup run until it completes.
More infö in this Apple Support document.........https://support.apple.com/en-us/HT201250