If you have the cap room, that isn't the issue. The Bengals have $46 million in cap. So they have enough room to tag and trade or tag and try to get a new deal with him if they want. I don't think they want to go into the season without a deal because he will definitely be gone in 2026 and they cannot tag him because they would have to make him the highest paid player in the NFL based on the 2026 salaries.
Again, if they cannot get a long term deal done in the next few weeks or months, there is next to zero chance that Higgins will be there in 2026. Then the most they can get in compensation for him is a 2027 third.
If they tag and trade him, they are likely to get a second rounder or more for him. I don't know if he could get a first based on what was reportedly offered for Aiyuk. But a 2025 second, especially the Patriots' second, is far better than a third in 2027.
As for Higgins fighting the tag and trade, it would depend on a lot of things. Would be willing to go to the teams looking to trade for him? Would he be mad that the Bengals took away his ability to be a free agent and pick whatever team he wanted? Is there a team he would really want to go to if not the Bengals who aren't willing to give up draft compensation, but would sign him as a free agent?
Now I don't know if the Pats would even want to get into a trade situation for Higgins. Higgins without giving up a good draft pick or two or three is one thing. Having to give up draft capital is another. They may feel Higgins is worth the draft picks and salary. Maybe then they made an attempt to go after AJ Brown and over compensate the Eagles or go after DK Metcalf or another WR that might be able to be acquired in a trade situation.