Is it normal for deck joists to just sit on scrap blocks like this?

While the boards are up, also check every hanger for the right fasteners, look for cracking or rot at the post bases where water pools, and grab the railing and give it a hard shake. The previous owner almost certainly knew exactly what he was telling you, by the way. 'It's to code' from a seller with no permit records behind it usally means 'nobody ever checked.'

To answer your actual question, no, a screw sideways into blocking is not support. That joint either needs a proper hanger or the joist sitting on top of the beam. When I redid my brother's deck two summers back we found 4 out of 16 joists just toe-nailed like yours, and every one of them had started to sag where the nails worked loose. Since you're pulling boards anyway, eyeball the ledger where it meets the house. Mine had no flashing at all and the rim joist behind it was soft enought to poke a screwdriver into. That's the failure that actually drops a deck, not one sloppy joist.

For what it's worth, when we bought our place I took the seller at his word too and never checked anything. First summer I noticed a slight bounce in one spot, and by the next spring one corner had dropped almost an inch. Ended up jacking it back level and sistering two joists. The thing that actualy saved me time was a cheap inspection mirror and a flashlight, shoving them up under the rim from below. Found lag bolts that had never been tightened, just finger snug. Worth doing the whole underside that way before you reseal the boards, takes maybe half an hour.

Seconding the guy who said the screw into blocking doesn't count. Same deal at my old place, previous owner had one joist just nailed to the face of the beam and called it a day. I put a proper hanger on it with the right structural screws and the difference was night and day, no more soft spot underfoot. Whole fix was maybe an hour and one trip to the hardware store, so if you find more of these while the boards are up, don't overthink it. Also worth a call to your town building department, they can tell you in five minutes wheather a permit was ever pulled for the deck.

Might be worth a quick call to your town's building department. I did that when I bought my place, asked if there was ever a permit on file for the deck, and the guy literally laughed. No record at all. Cost me nothing and told me exactly what kind of seller I was dealing with. Also, if it turns out there's no permit, some insurance companies get funny about claims if something happens on an unpermitted structure. Doesn't mean you have to tear it down, usually they'll just want an inspection or a retroactive permit once you've fixed the sketchy bits.

Update: got the rest of the boards up over the weekend. Found two more joists in the same shape as the first one, so yeah, built sloppy from day one. Took the advice here and put proper hangers on all three with the right structural screws instead of messing around with screws into blocking. Also gave the railing a hard shake like one reply suggested and it held solid, small mercies.