Good question, and I’m not sure. In comparison to a pour over, the majority of the extraction will take place during the immersion phase, so I would guess shape doesn’t matter as much. A conical brewer typically has a faster draw down compared to flat bottom, which may benefit you as you’re trying to remove the coffee when the immersion phase is complete. But this is all speculation!
I like the Switch because I can tinker with different recipes easily, adding an immersion phase at different points. Check out Tetsu Kasuya’s “God Recipe” for one idea.
I agree with some other comments here that $100 won’t get you what you’re hoping for.
A better upgrade would be to start saving for a good handheld burr grinder (like an 1zpresso model) to replace the blade grinder. Your French Press and AeroPress will likely taste notably better!
If you do want to venture into good espresso, as someone else mentioned, start looking into Cafelat Robot or Flair. Both can make fantastic espresso at higher quality than semi-automatic machines of the same price point and require much less upkeep. But, for any espresso, you will need more gear (scale, tamper, vessels, etc.) which adds to the price. And all espresso machines will massively benefit from a good grinder.
Good luck!