EDIT 18:50:
NEVER attempt a DOWNGRADE (like from Android 13 to Android 12). From what has emerged over the last 1-2 years in this forum, downgrading to an older security patch level can hard brick your phone (which can only be fixed by Fairphone's Repair Service for a fee).
Have you considered the OTA sideload option here:
https://support.fairphone.com/hc/en-us/articles/18896094650513
I noticed that the required OTA file is not available in the article yet, but Munich Fairphone Angel @AndreasChris has come up with one here:
Software update: FP4.TP1V.C.073.20230905 | Upgrade to Android 13 - #18 by AndreasChris
P.S.: About Fairphone Angels: 👼 The Fairphone Angels Program and Map (Local support by community members)