No access to The Sims Medieval

I purchased The Sims Medieval in 2015 for PC. I have only ever had one EA account and have never changed the email address or even account ID. I have played the game across two different laptops. I recently purchased a new PC (running Windows 11) and when I load the game from my EA app the game will not start. It seems like it tries to start but doesn't and just reloads the EA App. I have uninstalled and reinstalled both the game and the EA App several times. I have spoken to EA customer support via the chat function numerous times (three times I believe, once a few weeks ago and then twice tonight). The first time I spoke with an agent he gave me a variety of advice that did not work, including deleting numerous files from the game.

Tonight, when I spoke with EA support both agents I talked to told me that the game was not loaded to my account. They requested to see an invoice for purchase of the game, which I was not able to provide as I purchased the game a decade ago. When I was unable to provide them with an invoice I (one that I should have no reasonable expectation of still having literally a decade later), I was told that there would be nothing they could do for me and that I would just not have access to the game I paid money for. I literally do not even have the option to purchase the game again, since it is in my EA App as though I bought it (which I did). I've attached a screenshot with the game showing as purchased in my library and including my EA ID in the image, since I can think of absolutely no other way to prove that I own a game I bought ten years ago. How can this game be reloaded to my account? The second help agent I spoke to told me that my only other avenue of help is this forum.