How to find a lithium ion battery manufacturer? Can't find any samples online that aren't cylindrical (18650) or lithium polymer (lipo)?

I've been really struggling to find a battery that works for the product I'm designing (basically a belt buckle with a battery that powers some perephrials for a specific use case).

Every manufacturer I've found that has samples with dimensions on their website for batteries they make are either lithium polymer (not reliable enough for recharging) or cylindrical li-ion batteries (won't fit in a belt buckle).

You'd think it'd be easy to find a small, flat lithium ion battery (I believe they're called "prismatic cells" - ideally 2000mah - 3000mah & about 2in x 1.5in x 0.5in aka 50mm x 38mm x 13mm); it's basically the size of the battery in an iPhone mini. But consumer grade hobbyist batteries appear to only be available for flashlights and such and therefore are the wrong shape. And I can't ship a cheap, unreliable battery to my customers knowing it won't last as long as they'll expect.

Any suggestions on how to find a small li-ion prismatic battery that I can use to iterate on my designs?

Tl, dr: I need a flat, prismatic lithium ion battery (NOT lithium polymer / lipo and NOT cylindrical / 18650) but can't find a manufacturer with smaller enough samples on their website. Any tips on where / what to look up?