Quite a number of users here have a Fairphone 3, so perhaps you should let us handle the Fairphone 3 stuff 
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Yes, TWRP is available for the Fairphone 3, I use it myself.
But on the Fairphone 3 you usually don’t install it, because installing it results in a changed boot partition, as there’s no recovery partition on A/B devices.
A changed boot partition breaks OTA updates when using Fairphone OS, and in case of using /e/ it will just get overwritten by /e/ updates with the LineageOS recovery (or future /e/ recovery) … so there’s not much sense in installing TWRP on the Fairphone 3, so the Fairphone 3 usually doesn’t have it in recovery mode.
Booting TWRP with fastboot works, but like I said, please be more careful with assuming everything would work with every phone.