Research from the Fraunhofer Institut shows that in Germany, tire wear is the single largest source of microplastics, and it's much larger than the next source which is -- wait for it -- abrasion of plastic from road surfaces.
Sounds like Germans like to burn rubber (except that car tires are no longer ctual rubber but a composite containing lots of plastic).
https://www.celticwater.co.uk/bloghow-does-plastic-get-into-the-ocean-plastic-pollution-from-roads/
But back to doing laundry:
Several people have suggested using laundry sheets.
I had to look up what they are; they sound like a cool solution but then I found this:
"PVA is woven into laundry sheets to keep them intact. "
https://www.blueland.com/articles/are-laundry-pods-and-sheets-plastic
I'll stick to liquid soap.
But now I will also try the liquid laundry soap that my health food store sells out of a large vat with a faucet. BYO container: I can make that a glass bottle.