What display driver are you using with these, something like the SSD1315?
Most display drivers for these small OLEDs support both I2C or SPI communication. It should be reasonably possible to drive many of these displays if you use SPI mode on the driver, with a single SPI peripheral and one chip select GPIO per display. It would also be possible (but annoying) with I2C but you'd need one or more I2C multiplexers, since the I2C target address on these displays is typically not configurable.
Unfortunately, I do not know what driver we are using for the project as we're still brainstorming. The only thing I know is we need to fit a micro processor, battery, and screens, in a shape slightly smaller than a baseball.
Can you take a picture of the front and back of the screens, or link to the screens you are considering buying?
The screens themselves don’t handle the communication, they have a little driver board attached. Most of the driver boards have a jumper to change between i2c and spi mode.
DESCRIPTION This Wireling lets you display text and images via a 0.42" OLED Display! This 72x40 pixel screen features white pixels on a black background and is controlled via the I²C bus. The screen uses an internal boost converter to achieve the higher voltages required to drive the screen, so...
tinycircuits.com
Might not use these, but will use something similar.
I would recommend finding a version of this screen with the SPI connections broken out, and use SPI instead of I2C. The reasoning behind this is that the RP2040 has plenty of GPIOs to drive a ton of Chip Select pins for SPI devices, whereas using I2C will require a solution for multiplexing I2C addresses. The driver chips on these little OLEDs typically have a single fixed I2C address