Do you also have the Unofficial Dragonborn Patch installed (separate from the Unofficial Skyrim Patch)?
If not, install it. One of its fixes is:
Dragonborn's changes to DragonActorScript.psc have now been properly
merged with the fixes done in the USKP. Dragon soul absorbtion is now
working 100% correctly.
According to the Unofficial Dragonborn Patch's mod description, the load order should be like this:
Skyrim.esm
Update.esm
Unofficial Skyrim Patch.esp
Dawnguard.esm
Unofficial Dawnguard Patch.esp
Hearthfires.esm
Unofficial Hearthfire Patch.esp
Dragonborn.esm
Unofficial Dragonborn Patch.esp
HighResTexturePack01.esp
HighResTexturePack02.esp
HighResTexturePack03.esp
Unofficial High Resolution Patch.esp
Also as a reply to this answer, you shouldn't load Dragonborn after USKP, as it could undo the fixes of USKP. If unsure, just let LOOT take care of the load order.
Install the other Unofficial Patches if you have their DLCs too: Dawnguard, Hearthfire, High Resolution DLC.
Also, see the troubleshooting steps for the 'cannot absorb dragon souls' issue listed at the Unofficial Dragonborn Patch Nexus forums sticky post by Arthmoor, one of the UDGP developers:
Check for: dragonactorscript.pex
and/or mqkilldragonscript.pex
. Remove them if present. They are from dragon mods that came as loose files.
DSAMG - Dragon Soul Absorb More Glorious, and Diversified Dragons are known to cause this. Those mods need to be updated with a Dragonborn patch that incorporates the fixes from the UDBP.
Skyrim Unbound will cause this as well due to the script being unaware of the changes for Dragonborn.
Others may be a factor as well.
Note too that the offending mod may have the script packaged inside a BSA. That will need to be handled by that mod's author.
If you are using Mod Organizer and are here to report issues with dragon souls, sorry, but you're on your own as we do not support issues caused by incorrectly letting that program modify the BSA load order system the game has. Your post is likely to just be ignored. We don't have time to keep fending off false bug reports caused by people who insist on unpacking their BSA files using the program and thus subverting the entire system the game relies on for proper behavior.
The prerequisite quest for The Temple of Miraak is Dragonborn, which as you correctly suggest is triggered by reading the orders of the two random(ish) encounter Cultists who attack you in Skyrim. However, the prerequisite for the Dragonborn quest is not level related but requires your character to have started The Horn of Jurgen Windcaller for the Greybeards in order to be triggered.
If you visited Solstheim before starting The Horn of Jurgen Windcaller (even if you then later started and completed it) then UESP suggests that you must return to Windhelm and talk to the ship captain, Gjalund Salt-Sage, again to proceed in the quest.
Best Answer
Try one of these: