I take a slightly more narrow definition of “thoughts” that may be more akin to “expressions” - ideas that can be communicated, so excluding non-linguistic mental processes. I think that may be where we disconnect. A lot of my idea about thoughts comes from the Borges story, Funes the memorius (short story about a dude who could not forget - interesting read and really clarifies my feelings on my definition of “all possible thought”). In the story he talks about tree leaves, but instead imagine needing a unique linguistic scheme for every single unique snowflake you ever see. It would be a linguistic nightmare! Therefore language must generalize otherwise it becomes noncommunicable and that generalization to me induces the “lossy approximation” I attribute to language in my prior comment.
So, in my head Funes’s mind represent the abstract space of all possible thoughts. When we use language, we are stacking words/sentences/paragraphs/etc together almost like vector addition trying to reach a particular point in the thought vector space. Some languages have really clean ways of getting to certain thoughts while others take a mouthful and still don’t get you exactly there (物の哀れ example from link).
I agree with your statement on new languages being different thinking. As you follow that vector addition process to get to the “thought,” different languages will take you on different paths to get to your destination thought because languages encode those vectors differently, even if the destination thought is the same. In my mental model, the act of thinking is putting those language vectors together and tracing their path to get to your thought.
And if my comment still makes no sense - I might have to incubate this thought a bit more :) but I do recommend the story- it’s a quick, thought provoking read.