It's not a straightforward equation, but yes, there is definitely a trade-off between trailer weight and weight in the van. To calculate weights by the book, there’s GVWR, GAWR and GCWR limits. You want to make sure none are exceeded.
I have to make some assumptions here, as I don't have specific empty weights. Let's start with the GVWR. The manual lists a vehicle capacity of 1170-1420 lbs. Google says the base curb weight of the Sienna is 4610 lbs. Assuming this is for the lightest model, and that all models have the same GVWR (bad assumption, but probably decently close, then this implies a GVWR 4610 + 1420 = 6030 lbs. The actual GVWR is listed on the sticker on the driver door. But for this example, we'll assume it's 6030 lbs. If @djaral
updates with his door sticker GVWR, I'll update the math in this post. With this GVWR, I'm assuming the difference in people/cargo weight (1170-1420 lbs) in the van is due to differing curb weights of the vehicle.
Tongue weight is weight held by the vehicle, so your 1170-1420 lbs, with 350 lbs tongue weight, becomes 820-1070 lbs.
Now we'll consider GCWR. This is 8995 lbs for AWD. We'll use 4610 lb base weight + 1070 lb cargo + 3300 trailer = 8980, which is 85 lbs over the GCWR of 8895. So we have to adjust maximum cargo capacity down a bit. Assuming my assumptions are correct, this means with the OP's 3300 lb loaded trailer weight, the OP is limited to approximately 735-985 lbs of cargo and people in the van.
So the OP is on the right track, and not far off, but may be a little on the high side after considering GCWR, GAWR, and GVWR. Certainly they have a better handle on this than a lot of people I see towing trailers, so bravo! Keep it up @djaral
GAWR is much harder, there's too many variables to give a number in a post like this, so GAWR needs to be checked on a scale. GVWR and GCWR should be checked on a scale too. There's plenty of articles on weighing, but the basic is load the trailer and vehicle as you would for a trip (all cargo, all people). On a multi-axle scale (like for semi trucks), weigh the connected vehicle + trailer. Position the van so the front axle is on one scale, the rear axle on a second scale, and trailer on a third scale (if possible). This will give you your total van + trailer weight (GCW), compare this to the max GCWR of 8895 lbs. Verify each van axle weight against the GAWR listed on the driver's door. Finally pull off, disconnect the trailer, and weigh the van by itself to ensure the GVW is less than the GVWR on the driver's sticker. If you use a weight distributing hitch, there's a couple more steps in the weighing process, but the OP hasn't mentioned that, so we won't cover it here.
My 2020 Silverado I used to have, was rated at 9600 lbs towing weight. However, it basically boiled down to if you had the full 9600 lbs in a trailer, the truck was limited to 2 average adults and a small
amount of cargo, even though when not towing, the truck had a cargo capacity of about 2200 lbs! Towing 9600 lbs, carrying 4 adults plus cargo in the bed? Nope, you'd be WAY over the ratings.
In any case, make sure you have a good trailer brake system, and take a few minutes to ensure the brake gain is properly adjusted for maximum braking without locking up the trailer tires. I consider trailer brakes far and away the most important part of towing heavy loads, because if you need to stop fast, you need to be able
to stop fast.
Driving ~25 MPH, manually apply full trailer brakes with the brake controller, without applying vehicle brakes. If the trailer tires lock up, decrease brake gain and re-test until they don't. If they don't lock up, increase brake gain and re-test until they do, then step the gain back down until they don't. If driving on dirt, gravel, or wet roads, re-test and step the brake gain down, as the trailer tires will lock up much easier in these cases. The goal is to find the point of maximum trailer braking without locking up the trailer tires, as locking the trailer tires will greatly reduce braking force, and trailer braking systems don't have ABS, unlike your van, so once locked up, they will stay locked up until you reduce braking force. When properly set up, I could brake just as fast
when towing a ~9000 lb camper with my Silverado as I could when driving the Silverado unloaded, and that camper weighed 180% of the weight of the unloaded truck! Trailer brake importance cannot be understated!