This is a good deal, even if he doesn't play another NHL game ever. He's great in the AHL and that helps your prospects develop in a winning atmosphere. If he is anything more than just an injury call-up, then it is a massive win.
On the other hand, they have $120,000 in cap space and they NEED to sign at least one more player. They need to dump cap space and there's very few teams that can help them out.
The Senators would benefit immensely from opening up cap space, but they may not need to dump cap space to sign Pinto and become compliant. They currently have a 21 player roster with 121k of cap space. Capfriendly shows 19/23, but that is because they don't count the IR bodies (but they still count towards the cap). Activating Norris and Forsberg brings them up to 21 without changing the cap situation.
The worst case scenario plan is likely to waive both Brannstrom and Joseph. Both will clear. That will bring give the Senators approx. 2.371M in cap space with a 19 player roster. While Pinto apparently wants 2.5M x 2, Frost and Lafreniere both signed for less than 2.5M. It isn't unrealistic to thin that the Senators might be able to get Pinto down to 2.371M or a bit less.
That would put the Senators at a worst case scenario where they will run with no healthy scratches until an eventual major injury to a consequential player allows them to raise their cap ceiling via LTIR and recall a few additional players because for example if the player hurt has a 2M cap hit, that's enough to recall 2 2-way players instead of 1.
If there is a trade market for Brannstrom, they would open up enough to roll with a 21 player roster, but it isn't guaranteed that anybody will take Brannstrom at 2M. Very few teams have cap space, and he isn't exactly a blue chip prospect at this point. I think it is more likely that Brannstrom ends up on waivers and clears, and combined with Joseph clearing, they use that to open up the cap space needed to fit Pinto in.
Forsberg would be an alternate option to waive instead of Brannstrom, and it night make sense given the kind of injury Forsberg is coming back from. Give Sogaard some more NHL experience as the #2, and allow Forsberg to start games in the AHL in order to get back to top shape. Forsberg would almost certainly clear due to his cap hit, term, and the injury he just sustained. Only a handful of teams could claim him cap wise.