Nice images,
Typically the CHL sits in the interval area anterior to the LHBT and the superior glenohumeral ligament sits on the medial side of the LHBT tucked in slightly underneath it and these two structures are connected together forming the “sling”. I don’t typically expect the CHL to extend down as far as the structure in your case but do you agree it links exactly the same texture and sonographic composition.
So I am floating the idea that the structure might well be CHL and in real time you could see if you can follow it back to the CHL. It would be a little anomalous in terms of classic anatomy but nothing surprises me anymore!
The fluid does not make a diagnosis of tenosynovitis, but rather it is just GH joint fluid and may well be physiological given the volume. Tenosynovitis requires that the fluid have some synovial proliferation and vascularity. If the structure was a thick tendon sheath due to tenosynovitis it probably should have had some vascularity
Steve