I know this, you know this, Biden knows this. But the AOC, Bernie Sanders, and Elizabeth Warrens don't seem to want to give it up and let the bill move on. As you mentioned it is political theater but the Dem's are on a time crunch and can't afford to screw this up 14-3 fast approaches.The $15 minimum wage will likely be disallowed by the Senate Parliamentarian, which is what most people expected from the beginning. This would be a good thing because $15/hr, while OK in cities, will not work in rural areas.
Biden has already stated that it will be likely pulled from the stimulus bill. He’ll probably submit it as a separate bill to appease the liberal wing but it won’t go far. It’s political theater for the most part - Dems don’t have the votes.