The Wonder Boy dev said he was only influenced by his obsession with Wizardry for Monster Land, although he had played a lot of Dragon Buster and Tower of Druaga even though he apparently didn't like them much.
https://hg101.kontek.net/wonderboy/wonderboy-interview.htm
So many games copied various things from Dragon Buster (jan 1985) that I think they became ubiquitous quickly. Zelda II *may* have been the first to take the downward thrust though.
Miyamoto actually conceived Zelda II as a sidescroller with up and down attacks including the thrust, so it's possible the Zelda II we got was literally Miyamoto being inspired by Dragon Buster. He seemed to look at Namco games - see Devil World, his and Tezuka's first team up.
And some aspects of Zelda 1 like the way the shield works are straight out of their Tower of Druaga. If you are using your sword a projectile will hit you from the front, otherwise your shield will block.
Back on my Dragon Buster tangent, as far as I know it also introduced the Mario 3 style map to Japan
You can see the Famicom version added an axe item you could find to change your route
Here are some level maps to give people an idea, some straightforward others labyrinths
Anyway, inventing the double jump is all that needs to be said.
An interesting aspect of Tower of Druaga and Dragon Buster to me, is that they were influenced directly by western home console action adventure/RPG games that I feel like people gloss over as irrelevant to history.
Namco had an Intellivision and imported games for their devs, and the creator of Tower of Druaga literally played AD&D on it and decided to make that game. And his sequel Return of Ishtar is strangely similar to Swords & Serpents on the Intellivision. Both are two player focused dungeon crawlers with a magic user and warrior, with the magic user learning spells you find along the way, such as breaking through walls (which is actually in Druaga 1 too). Or a spell to temporarily freeze the enemy so the sword user can finish them.
And the famicom only Dragon Buster 2... is a straight up reimagining of Cloudy Mountain on Intellivision, no exaggeration. Down to small details that they are practically the only two games to share, such as no music in levels because you need to hear which type of enemy is off screen. Even the distinctive shape of the levels, the shroud, and a focus on arrows that you can shoot off the walls and kill yourself with on accident. Watch some videos of them, it's eerie.
Here is the axe in AD&D, letting you travel through forests in the overworld, there's a raft too to travel on the stream. Maybe that whole gameplay beat in Japan came from here?
A last tangent, the AD&D dev also made Alcazar which had similar stuff but with overhead dungeons as the levels, it was ported to the MSX for Japan in 1985.