Nope, not possible on the Fairphone 4 at the moment, and a weak point in general in all of Android.
If you want to get close to that, currently you would need
- an unlocked bootloader (did you lock it? Unlocking it again would wipe your data) with the accompanying security implications
- a TWRP build for the Fairphone 4 (you can follow proceedings here)
- TWRP support for decrypting the data partition (which seems to still be missing currently, and is not guaranteed in TWRP anyway).
The unlocked bootloader would enable you to boot TWRP, TWRP would enable you to
easily make backups of the relevant phone storage partitions, but TWRP most importantly would need encryption support to include the data partition in the backups.
Then keep in mind that TWRP doesn’t backup Internal Storage, but e.g. supports MTP to let you copy it via USB.
When all requirements can somewhen be met, though, you can come close to what you want.