Most likely the sewer line is clogged and needs to be cleaned out. Snake the sewer line all the way to the street. Could be clogged with tree roots. Not sure if motorized routers can be rented or not. If not, call a plumber.

Hubby has a GT Water Products Drain King clog buster that we have successfully used a couple of times to clear a slow/ partially clogged drain.

https://gtwaterproducts.com/index.php/drain-king/

I'm far away from home right now so can't check it for which one of the products shown at the link that we have. Various sizes for different drain sizes. Worked good for the utility sink that our washer drain hose empties into. I now keep a lint sock on the washer drain hose to keep most of the lint from going down the drain & contributing to clogs.

The last episode of slow drain at the laundry sink was due to a build up of hard water deposits in the drain line and P trap. Mentioning it as another possible cause of a slow drain. May not apply to your situation. (I would not have believed that it was possible for that much lime scale to accumulate in a drain--seeing was believing, though.)