You should be good to go on service size
I ran a quick load calculation with your square footage, 4 kitchen + 1 laundry circuit (counting GD+DW as one SABC and treating the fridge as lighting load), and stated loads for the oven and A/C units, and came up with just under 110A @ 240VAC, so you have plenty of room for your swim spa.
With that said, you'll want to plan ahead now to avoid future headaches
Your service entrance panel appears to be a version of the Square-D SC2040M200C, which means that you have to plan a bit differently for upgrades than folks with regular panels, as your main panel only has a single column of breakers, and is limited to 100A breakers maximum by the limited wire bending space adjacent to that column of breakers.
So, in order to provide enough room for a future subpanel to handle most of the lighting loads, I'd not only swap the top quad breaker to a HOMT215230 and move the disposal and dishwasher circuits there for the time being, but take the opportunity to either remove the dryer circuit, or consolidate it with the oven circuit by replacing the oven breaker with a HOMT230230. This way, you not only free up room for your swim spa, but a spare pair of full-width slots for feeding a subpanel in the future (you'll need it if you want to retrofit AFCIs, if nothing else).