"Too" is used in the first sentence as an adverb of degree, modifying the adjective "long". "Too" adds the idea of excess. "Too long" means excessively/overly long. (A consequence may also be implied or stated e.g. I wasted time/ the day grew late / I forgot to do something important...) The phrase, "a long time" is neutral.

Not quite. 'too long' implies that something has happened because we sat the same way for a long time. We can simply sit in a certain way for a long time. Or we can sit a certain way for 'too long' - ie, i sat that way and my leg went dead etc. If you just said 'I sat that way for too long.' without any extra information someone would say 'Too long why?' or 'Why was it too long, what happened?'