TWRP for the Fairphone 3 is official, instructions are here … Fairphone 3.
Be aware that TWRP doesn’t backup the Internal Storage, you would have to make a backup of it via other means (e.g. via USB when TWRP is booted) … What is EXCLUDED from a TWRP backup?.
Just boot TWRP with fastboot like you did already …
A/B devices like the Fairphone 3 have no recovery partition, so installing TWRP will alter the boot partition instead, to different effects with different OSes.
Fairphone OS for instance will not OTA update anymore after that.
/e/ for another example will just overwrite the boot partition with its own one (including its own recovery) with the respective next update.
If you choose to keep your bootloader unlocked to be able to fastboot boot TWRP when desired, this has security implications … How to lock the bootloader when the process is over? - #3 by AnotherElk.
Otherwise the process is pretty simple:
- Make sure to keep the install file(s) for the installed OS version (for a restore in case the OS partitions can’t be restored successfully with TWRP, better safe than sorry).
- Make a copy of the whole Internal Storage (because).
- Make a TWRP backup of your partitions, most importantly the data partition.