This can be determined easily from the bootloader screen, the screen with big green “START” at the top. The bootloader is reached from
Shut off your phone and press Volume Down + Power Button
If the phone is locked and you unlock it, the phone will have all data wiped.
This HowTo [HOW-TO] Flash /e/-OS on Fairphone 3 using Debian based GNU/Linux explains with images.
@piero linked the OTA update file which is quite different from the install ROM which you had linked.
The OTA ROM might work in one of the methods here …
but the install ROM is not made for this … the main a plausible reason for your fail.
Platform-tools would allow you to try Method 4.
On Fairphone 3 use of TWRP is an expert solution and sure to give problems while the bootloader is locked.
That would be correct if you could apply the OTA upgrade ROM successfully without any need to format or wipe data (as this thread proposes). Edit Beware that one could be put in a position where you format data (while hoping to avoid). So have a backup of essentials.
This is significant … and a good reason for caution.