If the total end run to the last panel is 150ft from the main I think you would be fine with using #3Cu for the sub feeds and using the called for #8Cu EGC. You shouldn't be loading the sub feeds to a max of 100A as a common practice, if so, you need a larger sub feed than a 100A.
I think it would be under 150 but very close. Anyhow, is there a huge size difference between 2 vs 3? I’m of the type who would want to play safe and overengineer things than to do bare minimum. At the end of the day, this is my house, its not like its a paid job.
Also siemens does not have a 115a breaker. A size higher is 125a and at that point, I am looking at #1 wire.
Things I would be running on these sub panels are big items such as car lifts, 5 hp table saw, 5hp compressor, press drill, washer/dryer, car dryer (master blaster).
Not all of them will be run at once obviously. Its not very easy to accurately estimate this stuff.