I highly commend the idea! As someone who has taught English in Japan (kinda sorta, DM me if you want the whole story), TA'd Japanese in the US, and has tried to tie video games with teaching foreign language, I'd like to offer a few bits of advice.

Netcode is Important

Smash is great but the netcode is AWFUL. Instead of more advanced algorithms, it just slows or outright freezes the game if anything is out of sync even a little. I could barely tolerate it playing with folks outside of my general region in the US (and often even within it). I can only imagine it to be unplayable between Japan and anywhere else.

If you wanna stick to platform fighters, I would highly recommend Rivals of Aether 2 (PC). It plays a LOT like Smash but uses rollback netcode, which makes for a MUCH better online experience.

I don't think I could ever win a tournament for either game, but I might be able to teach you a thing or two :)

The Zone of Proximal Development (ZPD)

I don't know your planned teaching strategy, so forgive me if you've already taken this into account.

Smash Bros is a pretty intense game that requires a lot of focus, even when playing casually. I can barely speak English when battling, let alone a language for which I'm not a native speaker.

It's a lot of pressure that I suspect would actively hinder language learning. You want to keep your learners in the ZPD, where they're not bored and not overwhelmed, to maximize their acquisition and retention.

I would recommend finding games where there's a lot of relaxed time between bouts of action or a game that's generally relaxed throughout that encourages conversation and banter.

Party games might be good options here. Mario Party (if it has a remote play option, I honestly don't recall) has all the board sections where there's plenty of time to converse (and commiserate lol). Something like Jackbox games might also work, especially ones that are more focused on creative input and not overly reliant on preprogrammed English text (there might be Japanese versions of this sort of thing, maybe?). Heck, you could even do Tabletop Simulator and play all sorts of games that make for a great learning atmosphere.

Turn-based co-op games are also interesting options. Sunderfolk might be a good option there, or even a co-op campaign of Baldur's Gate 3. The gameplay mechanics might make for difficult on-ramping for the language learning piece, but you'd certainly have plenty of content to discuss!

Willingness to play and learn

I think this is a really neat idea and would like to see you succeed. My ability to join is pretty limited though. Between a full time job and family obligations, I'm reliably available only between 9:30pm and 12:00am US Eastern Time (UTC-5:00 for now, UTC-4:00 during Daylight Savings Time), Tuesday-Sunday.

Best of luck!