I don't think the Monahan decision is all that impactful on the team's overall strategic direction in terms of youth vs vets or anything like that, especially when signing Monahan likely means the Habs will expedite a Dvorak trade, while trading Monahan probably means they'll keep Dvorak around longer as a vet C. All of Drouin, Hoffman, Dadonov, and Edmundson will be gone within the next two seasons, with a high chance that Dvorak and Anderson are both traded by then as well.
After the 2023-24 trade deadline there's a pretty real possibility that Gallagher, Matheson, Armia, and Savard are the only guys left from our current group of roster veterans. We're not likely to develop players to fill every single lineup spot, so I don't think signing Monahan is necessarily going to determine whether the team is going for youth or veterans.
To me it just comes down to the individual player's health and what the potential contract looks like. My preference is to trade him because I'm cagey about his injury history and don't really want to lock him in for 5+ years starting at 29, but if they have reason to believe his health issues aren't going to be a problem in the future or can get a 3-4 year deal done then I won't be upset about it.