Prediction: IF Switch Drake is releasing this (calendar) year, the reveal will be at the end of the month, in the Direct or a little before.
Both Switch OLED and Switch Lite were announced in early July with a September/October release date, so assuming a similiar window for the Drake, we should theoretically expect an announcement in early July. But holding a Direct at the very end of the June, showcasing games on old hardware, and then revealing their new stronger console a week or so later would be a very missed opportunity imo.
I think it's quite likely for Nintendo to push back their usual early July hardware announcement date by a week or so to coincide with the Direct, especially when it would be absolutely perfect to showcase massive titles like Xeno3, Bayo3, Pokemon SV, Mario Rabbids and (hopefully) BOTW2.
I don't think this is right, I'm afraid.
1. If you show off the upcoming games on the new hardware like you're suggesting, you are alienating your massive existing install base.
2. Point 1 is even more pertinent when you consider whatever Switch is coming next is likely to have very limited availability for a very long time. Limited due to likely huge demand off the back of Switch success, and limited due to the ongoing issues with manufacturing of parts.
If I'm Nintendo...
I look at my hardware sales. Still solid.
I look at my physical game sales. Still very solid.
I look at my digital game sales. Still growing fast.
I look at my subscription sales. Still growing steadily.
I look at the availability of components. Still a disaster zone.
I look at the PS5 and Series X rollout. Still a disaster zone.
I look at my own development studios timelines. Still all over the place.
I look at other studios. Still pretty sparse across the board.
I look at the economic situation in Japan. Oh dear.
I look at the economic situation around the world. Oh dear oh dear!
I reach my conclusion...
I really don't need new Hardware yet.
I'd love to be wrong, of course, but there is too much there to ignore. Throw on top Nintendo's Naturally cautious position, and yea, I think it's not happening.
EDIT: in fact, if there is to be new Hardware for Switch... the above all points to another budget version. Switch Lite OLED?