I think this is something you should fix first as I assume the mentioned commands should be run in fastboot and not in fastbootd mode.
Although it’s for FP4 and not for FP3 you might have a look at Black Screen/Booting Issue After FPOS C.073 Android 13 Update - #210 by GunniMator and the following posts as there at first the phone in fastboot mode was also not detected. But after changing USB port and rebooting the device again it finally worked… (and there are other things to check mentioned, too…)
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