Is my upstairs deck supposed to float like this?

An engineer is not overkill here. It's a few hundred bucks for a look at the framing, the cantilever length, and the condition at the wall, and you'll either get peace of mind or a clear list of what needs fixing before the family hangs out up there. Keep everyone off it til then, two chairs and a table is one thing but a barbecue with a crowd changes the math fast.

Had a similar setup at my old place. The joists just ran back through the wall and were bolted to the floor framing inside, which is probaly what's holding yours up too, even if it looks like nothing from below. When I opened up a section of drywall under mine I found the ends of those joists were soft as a sponge from water getting in at the flashing. That streaking you're seeing on the siding is the same tell. Before you spend money on an engineer, pull a baseboard or cut a small drywall hole under the deck and poke the wood ends with a screwdriver. If they're mushy, you've got your answer allready.

I'd push back on the idea that yours is probably fine because some other deck had joists running through the wall. That second reply even found spongy joist ends at the flashing when they opened things up, which is kind of the opposite of reassurance. The streaking on your siding is the same water path, so assuming the hidden framing is in good shape is a gamble. Also worth asking how far out that overhang goes. Past a few feet a cantilever gets dicey fast even when the wood is sound. You can peek from outside with a flashlight at the rim board or check the basement ceiling if it's unfinished, but honestly the guesswork ends when somebody acutally looks.

Update: took the second reply's idea and went looking from inside. Found a spot in the garage ceiling where there's an access panel, and sure enough there are joists running back through the wall, bolted to the floor framing. So that part checks out. But the third reply's point about the streaking got me, and when I poked the trim at the wall line the wood felt soft in one spot. Engineer visit is booked. Should I mention the soft trim specifically or just let them find it?