How do I know if my deck can handle a hot tub before I list the place for rent?

You're not overthinking it. A hot tub full of water plus six or eight adults is a serious point load, and a deck that was fine for a few chairs and a grill can still be marginal for that. The good news is you don't have to guess blind.

Start with paperwork. If the previous owner pulled a permit for the deck, the county or township building department will have plans on file showing joist sizes, spacing, and wheather it was designed for a spa load. Some jurisdictions even note hot tub reinforcement specifically. If there's no permit at all, that tells you somthing too, mainly that nobody signed off on it.

Then get eyes on it. You can learn alot without tearing anything apart: crawl underneath and look at the beam sizes, post spacing, and whether the footings are actual concrete piers or just blocks sitting on grade. Check for sagging between joists, rusted hardware, and any signs the hot tub sits on its own framing versus just resting on the deck boards. A hot tub on its own independent supports is a totally diffrent situation than one riding on the deck structure. Honestly though, for a rental with paying guests, I'd hire a structural engineer or a certified deck inspector to do a load assessment before you list. It's a few hundred dollars in most areas and it does two things: tells you if the framing needs beefing up, and gives you documentation you can show your insurance company. That second part matters more than people realize, beacuse if a guest gets hurt on a deck that was never permitted, the claim can get ugly.

Capping the guest count doesn't really solve your problem, by the way. Four adults in a hot tub weigh close to what eight do spread out, and renters will pack that deck regardless of what your listing says. Either the deck is rated for it or it isn't. Find out which before the first booking, not after.

Been thru this exact thing with a rental I managed for a buddy. His deck looked solid til we got under it and found the tub was sitting on doubled 2x10s at 12 inch centers, clearly added after the original build. That's the kind of thing you only learn by crawling around with a flashlight. Also, since it's a rental now, that slide off the railing is worth a second look. It was fine for your kids who knew it, but a guest's six year old going down it unsupervised at 10pm is the kind of thing that ends up on an insurance claim. Cheap fix: unbolt it between bookings or during the off season and stow it in the shed.

Decks from back before spas were common were never designed with any of this in mind. My old place had a deck built in the late 80s, joists toe-nailed into the ledger, no hangers at all. It held up fine for years until somebody parked a tub on it. Boards started crowding apart and you could see the frame bow just looking at it from the yard. If yours is anywhere near that vintage, assume it wasn't specced for a tub and let the engineer tell you different. Also worth checking if that sauna adds weight in the covered section, since those little rooms aren't light either.

Update: took the flashlight advice and crawled under there last weekend. Turns out the joists under the tub side look beefier than the rest, so somebody did think about it at some point. What I still can't figure out is the footings. I can see two of them but the corner closest to the slope disappears into dirt and brush. How do people usally confirm those without digging everything up?