Sxb, firstly horta Awdal is the Somali name for the ancient city of Zeyla, it may or may have not connection to the latter Sultanate of Adal(Zeyla predates Adal), secondly in the language of the Afar "Bill" is also a word meaning months, we know Afar were present in the town albeit in a smaller number from the sources I shared in that other thread.
As for the Adali clan not inhabiting the areas of Adal Sultanate today, my theory was that the land was called Adal before the Sultanate of Adal emerged in late medieval times, and the Adali clan probably migrated from the area they are named after before the Sultanate was born.
To be clear here I was not suggesting that Adal Sultanate was ruled or inhabited by the Adali clan or Afar in general.
Arab geographers used the word Awdal for Zeyla centuries before the Adal sultanate was established. I think your adal-adali theory is possible but not likely. My Awdal - Adal connection is also a theory but much more likely. Just thinking about this:
My theory: Adal comes from Awdal ancient name of Zeila.
Possible evidence:
1)Zeila the capital city of Adal is also called Awdal. 2)Arab geographers call the entire region Awdal. 3)Portuguese and other Europeans use the name Adel for Somali inhabited areas of north western Somalia. 4 ) modern day Awdal region is exactly the Zeila region and part of former Adal sultanate 5) scholars from the past say Zeila was inhabited by the same people as Mogadishu (somalis).
Your theory: Adal comes from the Adali clan.
Possibile evidence: the name resembles the name of the Adali clan, Herodotus said countries take the name from their people (but still isn't a universal rule) , Afars live close to Zeyla and used to live in the city.
Your evidence has several problems, first it's speculation with little text based evidence except some scholars who i admit connect Adal to afar words. Your theory about Adali afar migrating from present day Awdal is weak, Afar Homeland is northern Djibouti, southern Eritrea and North Eastern Ethiopia, Afars who lived in Awdal-somalia likely migrated from those regions and not the other way around