I think it has been made clear the Joneses do not believe in spending on free agents, regardless of the CAP situation. They have said as much repeatedly claiming that free agents are overpaid. Every year they find a free agent or two that costs them close to the minimum. They are completely inactive for the first 2 weeks of free agency. It has nothing to do with Dak.
But it is interesting that the OP does not include Dak's 2025 CAP hit of just under $90 million. That of course is going to hurt the Cowboys ability to spend in free agency. But it starts with their own guys. The Cowboys have a few free agents I am sure they would retain if not for the CAP. Guys like Lawrence, Lewis, Odighizuwa I am sure would be re-signed if not for the CAP. Signing Dak at a $90 million CAP hit is going to hurt. At some point, either this year or next if they restructure him again.
But unlike teh Eagles who are in a position to win multiple Super Bowls, the Cowboys are a long way from contending, which is why they should not be mortgaging their future now. Once they get closer to a winning team they can go all in.