Wheel's been pretty stale for many years to be fair. The Million Dollar Wedge is about the biggest change the show has had in a long while now. Not much else has, sans a few additions to the wheel here and there and the extra toss up this last season. Jeopardy on the other hand, besides Alex and his cancer giving them press, has had in the last 3 years.....the big All Star Tournament that brought back many big champions from the past, David Holzhauer's incredible and record breaking run and the GOAT series of games that followed that. What has Wheel had in comparison? Not much.
Jeopardy has done much more/had much more to keep itself in the mainstream than Wheel has, and even before all they they were/did I'd say with the various tournaments they've held (such as the Decades one for one particularly notable example when they had their 30th anniversary). So it makes sense they'd get more notoriety at awards time given that. They've been streaming some of their classic episodes too in addition, something Wheel has not done. So that surely has to help as well.
The whole reason for those big J! events is because of the show having returning champions. Harry Friedman took them away from Wheel almost immediately after he took over the show. Wheel could very well have had its own Ken Jennings or Jamrs Holzhauer or whoever, but we'll never know. People say Wheel shouldn't bring back champions because of how much luck is involved (yet nobody had a problem with Press Your Luck having champions?), but if they did, the show would be more popular again. I remember when everyone was talking about that guy who solved "NEW BABY BUGGY" with only the N and E, but it didn't bring more viewers to the show because it would be different, likely average players if you tried to watch.
Jeopardy!'s newfound fame is all because of both Alex as he fights cancer, and the big champions they recently had. I rememberr when Jeopardy had that guy with the big gray hairdo who kept making the funny faces (forget his name), he was talked about in the media every single day he played, and that was around the time Jeopardy started overtaking Wheel in ratings regularly, not just when they had Watson or 20-day champion streaks. Pat had his health scare, but he didn't get nearly the same amount of support (not trying to compare bowel obstruction to cancer, but either is no picnic), and even when Vanna took over for him as host, people thought she was bad at it, and Wheel still lost to Jeopardy in the ratings for the weeks that she hosted even though there was a lot of publicity about it. I thought it was great to watch her at least do something different, and I think the Emmys should have at least given Vanna some recognition in that regard by maybe giving her a Host nomination as well (even though she likely still would have lost to Alex). The only thing I didn't like was having Mickey and Minnie mouse just stand to the side while the letters lit up automatically.
Wheel is "stale" because of Sony not doing anything to give it spotlight. They just let the brief spotlight come and go after a funny answer, a last-minute dumb wrong letter, or a one-letter solve on a cliched Toss Up. Look at what was happening on both shows last May. Holzhauer was winning six figures in one game every other night, on a show that many fans complain doesn't give enough money for the contestants' knowledge and efforts, while Wheel, which was not being cross-promoted one bit, had a record losing streak in the bonus round. It was quite a difference watching somebody steamroll two players and win over $100K in one game, to going to someone expected to solve "WACKY XYLOPHONE GUY" and leaving with $15,737 cash and trip to some Caribbean island. And Wheel even had their 7000th episode during Holzhauer's run. It got some promo, but the show itself really didn't do anything much to celebrate it, compared to Price which always goes all out for its X,000th episodes. No special gameplay stuff, the same flashback clips they've been playing since the 4000th show, and a thrown-together bonus round puzzle that wasn't solved. Let's Make a Deal and TPIR's Mash-Up Week is a wonderful idea for cross-promotion, but the most Sony does with WOF/J! is the "Wheel of Jeopardy!" category every now and then.
As for the streaming, again, that is another thing that is entirely in Sony's control. They could definitely put classic Wheel up for streaming but they refuse to. But if streaming were a thing in 2000, I'm sure both shows would have been put up. Wheel and Jeopardy used to always get the same promotional deals, and now 90% of them are Jeopardy-only. But we know how Wheel is about their "classic" eras. Look at how Jeopardy reran some of Ken's original games recently, but Wheel has only gone as far back as 2017, and I bet many people can't tell the difference because Sony wants it that way.
Jeopardy definitely deserves more notoriety, but Wheel doesn't deserve to be pretended like it's off the air. What has Double Dare done to give it more recognition than Wheel? I liked the reboot, but I completely forgot about it until recently.