I think there is a difference between not extending a 33yo Pedro Martinez vs a 26yo Betts.
Not to mention, Epstein liked to take advantage of draft pick compensation rules back then for his Type A free agents, particularity the rules that allowed you to gain 2 picks for losing a Type A but only lose one pick for signing another one. It allowed him to rebuild the farm system while staying competitive. None of that was in play with Betts.
The problem is, the contract Betts was seeking and eventually received was not exactly out of line for his market. He was one of the best players in the game, and other lesser players are making close to what he makes. Gerrit Cole? Bryce Harper? This was getting to be the cost of doing business. Betts' deal with LA was more in line with the value of recent deals than the one the Sox gave Manny Ramirez 20 years earlier. And one that Henry paid despite it being one to set market value rather than follow it.
And, do you really think committing over $200 million to Eovaldi and Sale (and over $42mill AAV) had no impact on whether or not the team had budget room for Betts?