First, this response is 'top of head' and 'just enough' details ... might require further explanation depending upon your experience at command line.
It's good that you are consolidating from lower version of moodle to a higher one. But that's about the only plus.
Hope all 3 of the servers involved are linux - and that you have command line access to all of them.
The 3.11 server will require more resources ... for the initial consolation, more space. How much free space do you have on the 3.11 instance?
Once restored, they will be used, so that will probably mean some tweaks to DB server - so that would involve more memory. How much memory does the 3.11 have?
Another question about the old version server backups ...
Are they full course backups that includes users as well as events?
If an admin level user is enrolled in a course in the older versions, there could be
role conflicts when attempting to restore to the 3.11.
Plugins - 3rd party - does the 3.11 have already installed the add-on plugins the other 2 instances use? If not, install them on the 3.11 prior to attempting to restore.
You may not have hit the largest course yet!
Command line foo ... there is a utility for moodle called moosh ... command line only.
Install the one compatible with moodle version:
https://moodle.org/plugins/view.php?id=522
moosh is just php talking to the DB server ... web service is skipped.
One could make full course backups from the older versions, saving the backups to a directory inside a file system repo in moodledata/repository/xfer/ so you can see them by humanly recognizable names and see how large they are.
https://moosh-online.com/commands/course-backup
From moodledata/respository/xfer/
moosh course-backup 3
where 3 is the course id number.
Execute as many times as there are course ID numbers. Skip course ID 1 as that
is the front page of the moodle and that cannot be restored.
https://moosh-online.com/commands/#course-backup
To get a listing of course ID's ... a DB query from the cooomand line to dump to
a cids.txt file:
mysql -u $mddbuser -p$mddbpass -e "use $mddbname;select id from mdl_course;"> cids.txt;cat cids.txt
cids.txt consist of just the course id numbers.
On the new server, a file system repo is setup - call it restores - all of the backups from the older servers could xfer their backups to that file system repo so one can see them in the moodle admin GUI interface.
From old to new ... one could use either scp or rsync.
moodledata/repository/xfer/ to 3.11 server's /moodledata/repository/restores/
Using command line means no download only to have to turn around and upload via GUI - *SERVER TO SERVER*
Once you have a set of backups on the 3.11, one could use moosh again to restore them to a category:
https://moosh-online.com/commands/#course-restore
Note: I had to restore a 130+Gig course once and had to use some more command line foo:
nohup 'moosh_command_to_restore_here' &
nohup command means 'no hang up' - do until done. & puts the process in the background so one could actually log off the server ... log back in hours later to check on progress of the restore.
You are in for a lot of work ... non-prime time if they are all being used.
Remember that cron jobs for all 3 servers are running once per minute also.
Some cron jobs clean up moodledata/temp/backup/ the directory that is being used to build backup .mbz files.
Using command line is more efficient and overall faster than using GUI.
Lastly ... a comment ... 3.11 is very old. You might be in need of upgrading
the site after you get all those courses restored!
'Spirit of Sharing' (SoS), Ken