Tea isn't usually run through a filter (I make mine with filtered water, but I'd have to add a step where I pour the water through a filter before brewing). Only some coffee is - espresso and french press aren't). Not so sure about beer, I would guess many brewers filter the water coming into their tanks?
Right, lots of teapots also have a fine wire mesh to keep tea leaves from getting into your cup, but I doubt that'd be fine enough to catch 'chalky' microplastics. I would think espresso and French press would also need to have their water pass through a filter before coming into contact with the ground coffee.
Recent fad in espresso is to place a disk shaped coffee filter in the portafilter. Idea is to remove oils and smaller sediments but microplastics would get filtered too I guess. Though espresso machine would usually have soft water and this method doesn't work as well for soft water.
