There are different versions of the ATSAML22, for this purpose I have set my eyes on the ATSAML22G18A, it has the lowest pin count, meaning it's the smallest, while also having 256kB SRAM for programs. The amount of SRAM is probably not necessary in the end, but for developing it is good to know that you have enough space and can downgrade to reduce BOM cost. The chip has an integrated LCD controller with lots of options and 23 dedicated pins that are highly configurable - perfect amount for the 22pins of the watch LCD.

Another way of controlling the LCD could have been using the very well supported Holtek HT1621 and a controller of your choice, like maybe an ESP32 or a nordic chip. An Integrated LCD controller can also be found in the Atmega169, but it's an EoL product and the datasheet from 2006 says "Not recommended in new designs".