How often should you wash a teapot?

Every time you use the teapot. How you clean it depends on what material it is made of.

Glass or other non-porous materials like high-fired porcelains: soaps permitted, but probably unnecessary. Occasional baking soda or vinegar to descale.

Clay or semi-porous materials like crackled porcelain: no soaps, that would ruin your pot. Just flush with hot water. Very very occasional baking soda (no vinegar) if the pot gets seriously dirty. Perhaps you left tea in there overnight and the pot is unbearably stained over years and years of use.

Some pots made of clay or semi-porous glazes are meant to change as you use them. They take on a patina due to years of use. Therefore, you don’t really want to scrub them or use baking soda with any sort of regularity.