Somalia is Turkey's distant third theater, after Syria and Libya. Now that one is won, it moves Somalia up the list of priorities. It seems, for now, to allow them to pressure Ethiopia into doing their bidding.
I don't know why people are talking about him folding when HSM is in a relatively strong position. He got AMISOM out and more Turkey-Qatar-friendly nations deployed in Somalia in their stead. While HSM is very much overplaying his hand with Jubbaland, he is now the strongest president post-war we've had yet. Debt relief, arms embargo negotiations—he even got HSM to sign the 30-year lease on Somalia's territorial waters.
After outplaying Russia and Iran in Syria, he's doing the equivalant of camping at low levels to kill time until Trump is in office, and Turkey will likely play a key role in the Ukraine-Russia peace deal.
Turkey's also playing a role in the Sudanese civil war so Turkey's interest in Somalia as a springboard into that theatre is solidified.
When Trumps in office, the world will be way more destabilizied and fluid, so I can understand Turkey now, in Syria and it seems Somalia, to try and "solve" as many of their theatres before hand.
When it comes to the US and Somaliland, anything Somaliland can offer, Djibouti already has. The US clearly has put their lot in with the FGS and honestly for good reason, the last two countries, not that far away Eritrea and South Sudan ended up complete failures. Besides Somalia once pacified just is larger springboard.
Besides the US already has bases on and off record all around Somalia.