FWIW, my own personal take is not so far off from yours but is a bit more nuanced. Most of their resources/assets are locked in a development cycle in the minor leagues. Some of that is maturing into front line talent (Casas, Bello, Crawford, Houck, etc.) Some is coming in now. Some is due to arrive in 25 and 26 and so forth. Assuming all stays as is, they will have a multi-year window where they still control the players with more service time while younger players are coming into the majors.
Eventually it will start to grade out into free agency (Casas, Bello, Wong, Crawford, and Durran all are FAs after the '28 season.) Granted, that's a long time off in baseball time, and some might be extended or traded well before then. And perhaps the next currently-undrafted/unacquired Casas will be arriving in 2029. But the point is that while 2028 is a maximum saturation point, the club should have significant cost-controlled talent on the major league roster before then. Either this year or 2025, 26, 27, and 28. (But if those years are successful, it may prove harder to draft talent into the org.)
In any event, that's their window - 24 ramping up into 26-28ish. As far as FA's go, they certainly don't want someone who is going to be in the decline phase for years 26-28. So, they're going to want either longer contracts for ultra-premium star players who won't decline (YY perhaps), or short term FAs that won't burden the club in 26-28 when they're extending players or looking to fill gaps via the FA market.
Hence the short-term Giolito contract, and not going "all in" on someone like most of the mediocre-ish guys we actually might have landed but apparently passed on.
At the end of the day, you can only have so many premium FA signings. (Just positing that as the realpolitik financial reality here.) So why not look forward and save those 26-28 FA slots for players who will contribute. Not someone like a 33-36 year old Teoscar Hernandez. (I mean, maybe Teoscar will still be a good player then, but if the Sox internals indicate maybe otherwise, there's no need to sign someone like that today.)
The real question is while getting there, can they pick up short-term FAs (or players under contract) who might push them into competitiveness this year, next year. Again, Giolito. And O'Neill. And perhaps even Grissom. So I don't think they'll be dumpster-diving, so much as filling the roster with what short term FAs they can. When they get into a critical competitive window, that may change. Like if the team clicks and they're in the post-season hunt this year.