Welcome!
Congrats on your new sunny!
On your tires, there are a few things to check and see if they will fit.
1. Bump clearance from the tire touching the bottom side of the wheel well. Measure the gap from the top of the tire to the bottom of the fender well on the tires you have now. What is that distance?
Dexter axle recommends 3” is the minimum bump clearance but Sunline set up some of the campers with less than that. My camper only had 2 1/2” clearance when I got it. That does work but that is about the limit. 2 1/4” sooner or later can hit depending on how bad the bump was you ran over. Since your new tires are larger in OD that will eat into the available clearance.
2. The extra width, look inside now at your old tires on the distance between the tire sidewall at the widest point and the frame. As the trailer turns the axle flexes and the distance gets smaller but to small to not have the tire rub the frame. What is distance you have now? Since your new tires are wider, it will reduce this distance. You may be able to accommodate the width, but you neeD to make sure you have enough clearance at this area.
3. The wheels themselves, check that the new tire will mount in the rim width you have if you are not buying new rims. The tire manufacturer sets limits on rim width that their tire will be acceptable to mount that tire on. I would not recommend you exceed that limit as a wider tire on a too narrow rim that is not allowed can have sidewall flex issues.
4. If you get new rims/wheels, make sure they have zero offset as trailer wheels do not have an offset and the bearings and axle is made to handle only zero offset. (Offset is the distance the wheel lugs are from center of the rim)
5. The new tire can handle more load. Check that your wheel can handle the load of the new tire. Or get new rims/wheels to match.
If you can accommodate those areas, changing size should work.
I noticed you said ST tires, yes that is right for your camper and not the P tires it had oil it.
Hope this helps and let us know how you make out.
John