I would like to know if consoles like the N64 and GBA used masked ROMs or some kind of eFuse based ROM, or if they were some kind or flash or EEPROM based memory. I've read that both consoles had cartridge capacities up to 32MB in size, but the thing is I am having a hard time finding any MROM/PROM chips that ever existed larger than 1MB.
Well, for sure next to every storage variant - maybe except core (*1) - has been used with them by now. It's next to impossible that something possible hasn't been done, especially if this includes independent games, homebrew and development options.
Now, if the question is strictly about production games by/sanctioned by Nintendo, then the answer is a clear ROM ONLY. After all, even games that didn't sell were produced in quantities of 100k or above. That's way into the area where a ROM beats any other storage solution (*2)
or if they were some kind or flash or EEPROM based memory.
For one, FLASH was only stating to sell around 2000 (*3) and was quite expensive at the time, even compared to (E)PROM. Second, EEPROM was always expensive - and rather small, even 1 MiB was at the time next to impossible.
FLASH and EEPROM was only used to store save games, ad only starting in the mid 2000s.
It may surprise form today's PoV, but the ubiquitous FLASH (like) solid state storage isn't that old - and being dirt cheap even less.
I've read that both consoles had cartridge capacities up to 32MB in size,
N64 and GBA could fit up to 64 MiB.
but the thing is I am having a hard time finding any MROM/PROM chips that ever existed larger than 1MB.
There were no PROM of that size, and as usual with high-volume, professional-only products, information on the web is rather rare. you got to look into manufacturers datasheets. Maybe look for
- Macronix MX23L12810 as 128 MiBit/16MiB (x8 or x16) Mask-ROM, or
- Macronix MX23L25610 as 256 MiBit/32MiB (x8 or x16)
- Macronix MX23L51210 as 512 MiBit/64MiB (x8 or x16)
At that point it's also worth to keep in mind that GBA and N64 had a 16 bit wide data bus for their Game Packs, so a single x16 chip could provide the maximum amount available.
*1 - Caveat: never underestimate game tinkerers :))
*2 - Depending on size and product class, a ROM would have had a break even point already around 1000 pcs.
*3 - The first (reasonable number) consumer FLASH product was Sony's Memory-Stick in 1998, offering 'barely' 4 MiB storage at a ridiculous price.