For me, I'd not want it connected to the trees. The trees don't all move in the same direction at the same time and they will move a lot more than the building would by itself. As the tree grows, the connection to the tree can fail. Having the platform rest on the piece between the two trees and able to slide is better than having it bolted. We used to use some sliding connections when we built stands up in mulit-trunked trees but we've gone away from those stands to free standing towers or purchased ladder stands.
My biggest concern that I see is buckling of the legs or loosening of the connection between the legs and the platform or the platform itself. More bracing keeps each leg where it should be so it can't buckle and they share the loads. It looks like some of your platform's outside boards are bolted to the uprights but I cam't tell if they all are. If not, bolt each board to the upright at each end. Then I'd go to the hardware store and look at the various metal connectors pieces they have (like Simpson Strong Tie). Nail (not screw) those to tie the various pieces together for extra insurance.
https://www.strongtie.com/woodconnectors/landing. Nails are better than screws since the nail can slide out while still carrying load while a screw will shear and fail. If your platform is screwed instead of nailed, all the more reason to add nailed metal hangers, connectors and straps.
You got a nice building started that should give you many years of great memories. Spend a bit more time and effort to be sure it is safe.
Last question, are those ash tree around it?
