we gon' die

"influenza is really good at jumping between species"

What kinds of profiles do you like? Do you want a second hand, vintage set that may be more unique? What color palettes are you looking for? What boards will they go with? Do you need RGB shine through keycaps?

That being said, my vote is always for a Signature Plastics SA profile keycap in whatever theme fits the board.

How can one have a custom keycap set built?
By custom keycaps I mean keycaps with a custom geometry that doesn't exactly match the profile/shape/size of any existing keycap set.
I'm currently 3D printing such keycaps but I wonder how they could be built in (non-3D-printed) ABS or PBT.

The shape is not too exotic; they look kinda like this: https://adafruit.com/product/5111 but with some (nontrivial) differences.

Bonus question: how to add custom art/fonts/icons to the keycaps.

If you have to ask, it's too expensive. You're looking for a set of 100+ custom molds to be created for your unique keycap set. If you want doubleshot keycaps, it doubles the number of custom molds. You would be requesting a keycap manufacture to create brand new molds for for the profile you desire, plus the R&D of mold making. Unless you plan to sell your own keycaps using your unique profile, it would be cost prohibitive. I would expect no less than 10k and likely north of 15k for a one off, custom profile, injected keycap set.

With a few hundred to thousands of hours of work and access to a small desktop mill you could replicate what this user did and cast their own keycaps using lego and plastic/silicone molds.