Feels like I am stuck

I need some good advice. I have been working on a very weird project for past two and half years now. This project has not at all being in a proper way and feels like a classic case scenario of sucking up to clients to keep the business with them. But in this conundrum, I am suffering A LOT. My core working areas are SSIS and SQL Server and I have been trying expand my skillset to cloud platforms like Azure engaging in some proper Data Engineering roles. But I have been sole contributor in my role in this project and inevitably a very heavy dependency developed upon me over time and now the management is not willing to involve me in any project other than this. I have been trying to get some opportunities laterally but since I have no hands-on experience in my "preferred skillset", no one's willing to consider. I tried talking to my managers and I keep hearing "It's a good thing that you have developed such good rapport with the customers" (which I have), "this project will end soon and you will get better opportunities once we close this project", "we will consider you for on-site opportunities". None of these promises have been fulfilled. I realized very late that I have just been exploited since I have been doing at least a three man job in the billing of one and they keep extending me on the project. Accolades are there but just on mailers and that too from customers, not my managers. To add insult to injury when I received customer appreciation no one from the management even bothered to highlight it internally and they didn't nominate me for H1B unlike they promised. There is no incentive of any type- bonus, better project or onsite opportunities and I am struggling to find jobs within or outside the organization because of current market scenario and lack of experience. I am getting restless thinking about this and the time I am losing on this worthless project. There seems to be a huge disconnect between HR, management and employee. What to do???