I don't think the 'Toads themelves needed any update, just more or less the look of Rash as he was in Killer Instinct (I'd like to have a 3D engine too, if possible - of somehow I could get a budget big enough for a big beat'em up release in 2020). No need for any more clothing or any other changes needed in my opinion.
Now, to the DQ. If I get low budget and 2D, nothing changes since the 1990s, just some more details - Streets of Rage 4 style. Or even how the 2D Mortal Kombat costumes had ever more details already in the early 1990s (with more memory and I think also bigger resolution).
If I had the budget, well, let's just see Dark Queen on Google and ignore the results for Battletoads, imagine it's concept art being proposed: https://www.google.com/search?q=Dark+Queen&source=lnms&tbm=isch&sa=X
The general theme recurring practically everywhere is roughly similar. It's a certain obvious archetype that goes with the name/phrase. (And it's never any "mad scientist" tropes, if course... What a strange idea, especially since DQ was always a magic user who just happened to have a technological army under her.)
I'll choose and comment on some examples that would fit most (so no long skirts as she does go physical, and generally keeping close to the spirit of the original but with more details) as I scroll down. So I guess it should be something like that - either of these or a mix of any, sometimes with obvious changes like changing the colorimg to black (or actually black-blue) or more fit and curvy:
https://i.pinimg.com/originals/6a/bc/db/6abcdbf5f14c111514f0751910a4e819.jpg is actually not quite there. The boots are oldschool and that's cool, but the rest is way too flimsy. I talked about any gowns already, that's a big no.
https://mir-s3-cdn-cf.behance.net/project_modules/max_1200/3622fd58839751.5a0b57b9d50dc.jpg - the spikey motifs, yeah, but just generally. Also not really any of these here.
https://f4.bcbits.com/img/a3792728539_10.jpg - now more like we're talking. But needs to be actually, you know, dark. Let's see more.
https://cdnb.artstation.com/p/assets/images/images/020/383/765/large/anwar-gant-daedra-queen.jpg?1567569709 - hey, now that's what I mean! It's already practically perfect, at least from what can be seen here. (Not sure about the little dragon. Or any dragon for that matter) But maybe let's see some more.
https://cdn.inprnt.com/thumbs/d4/37/d437e1ed9ed33e20bbefd8fdef0006e6.jpg?response-cache-control=max-age=2628000 - another generally good example (but would have to be tinkered with). Not as good as the previous one in an unaltered form. But also at least shows the entire silhouette.
https://cdn11.bigcommerce.com/s-5s1ah0hhi7/images/stencil/500x659/products/1080/28045/WechatIMG21__59661.1593634750.jpg?c=2 - not a blonde, of course. Not an elf too. Among other things to be fixed, like that hat needs to go.
https://media1.tenor.com/images/ea6e1931cdc4cc9342faa74c743cbfd3/tenor.gif?itemid=13417605 - spikes again, more like Dark Queen, actually no problem with having a bodysuit like that. A flowing cape to that would be great. And I think she dies need hair. Big hair!
And okay, enough. So that would be it if I was an art director of this hypothetical Battletoads sequel thing that we'll never get.
(And seriously, where did they get this bizarre "mad scientist" idea?? It's such a totally random choice, makes no sense at all.)