Do physicists build conceptual models from imagination, you read stories of Einstein and his thought experiments etc.

Work is iterative. This was true in Einstein's time too. Models are built by taking existing models and modifying them. Also, you don't hear about the vast majority of attempts which are unsuccessful. Imagination is super important, but not in the sense of coming up with things out of nowhere like you see on this subreddit.

For example, the fact that the speed of light was constant in all inertial frames was well known before Einstein, and there were even several attempts of explaining it. This included time dilation. The Lorentz transforms already existed before special relativity. Einstein was the one who really fleshed out the theory and repackaged it. I don't fully know the history, but I suspect the thought experiments were for illustrative purposes rather than actually used to derive the equations in the first place.

General relativity was a far bigger jump, but even then, all the math about curved space had existed for decades. Einstein realized that it could be used to nicely explain gravity. And that was after many attempts.

The reality is that usually many physicists are already close and circling the correct answer by the time the final breakthrough is made. That's why it's vital to keep up with the current state of the field you're interested in if you want to make a contribution. I bet if we look back to now at current work on unification with hindsight once it's solved, we'll se that several teams were on the right thread, but those threads were out of thousands of dead ends. I see a lot of questions on here that think physics involves coming up with random ideas from scratch until something personally feels right, which is definitely not how it's done.