Welcome to the community forum.
You did perhaps miss that you can install TWRP on the Fairphone 3 as documented at twrp.me.
But usually you would just boot it with fastboot when needed, because installing TWRP on the Fairphone 3 alters the boot partition, and that has further implications depending on your OS setup. (Breaks Fairphone OS OTA updates, gets overwritten with /e/ stock recovery by /e/ OTA updates.)