Yes all correct 

Autoimmune thyroid disease, like Hashimoto's, can sometimes be associated with mildly elevated TTG levels, but it’s not the primary cause of a high TTG reading. Since celiac disease and autoimmune thyroid conditions frequently coexist, your doctor is right to investigate further. It’s encouraging that your TTG has dropped slightly, which may suggest some fluctuation rather than a definitive celiac diagnosis, especially with a negative EMA test and your prior negative endoscopy. However, the ongoing elevated TTG could indicate low-level inflammation, possibly linked to a gluten sensitivity or early-stage celiac that wasn’t yet visible during your last endoscopy. Since your doctor is consulting with a gastroenterologist, it sounds like they’re taking the right steps to ensure you have clarity. In the meantime, if you experience any symptoms related to gluten, keeping a symptom journal could provide more insights. This is a tricky area, but it sounds like you’re in good hands with a careful approach. For people with celiac disease hidden gluten in their diets is the main cause of elevated Tissue Transglutaminase IgA Antibodies (tTG-IgA), but there are other conditions, including cow's milk/casein intolerance, that can also cause this, and here is an article about the other possible causes:    

So, let me seek some clarification here. You have not been officially diagnosed with celiac disease. Even though you had elevated ttg-iga levels on three different occasions your endoscopy/biopsy in 2021 was negative so the conclusion was that you do not have celiac disease so you have continued to consume gluten. Is this correct? However, you have officially been diagnosed with Hashimoto's. Is this correct? And you are wondering if Hashimoto's can cause elevated ttg-iga levels. Is this correct?

Referring to Anti-tissue transglutnase and then iga antibodies . If that makes sense ?  yes eating gluten 

Are you following a strict gluten-free diet? When you refer to ttg I assume you mean ttg-iga and not ttg-igg?