Hi,
I also had a hard time booting into recovery mode.
In the end, I managed thanks to this Reddit post: https://www.reddit.com/r/LineageOS/comments/n0k6sn/fairphone_3_fastboot_error_boot_partition_is/
This command lets you know which slot is active (a or b)
$ ./fastboot getvar slot-active:a
slot-active:a: No
Finished. Total time: 0.008s
$ ./fastboot getvar slot-active:b
slot-active:b: Yes
Finished. Total time: 0.007s
If slot b is active, the following command will flash to the correct slot:
$ ./fastboot flash:raw boot_b ../lineage-18.1-20210816-recovery-FP3.img
Sending 'boot_b' (65536 KB) OKAY [ 3.207s]
Writing 'boot_b' OKAY [ 0.312s]
Finished. Total time: 3.592s
Then use adb normally to flash LineageOS:
$ ./adb sideload ../lineage-18.1-20210816-nightly-FP3-signed.zip