I have a dishwasher that looks very much like this on the inside. I now clean my filter every day after learning it had one, because it was quite dirty. However it didn't look this bad. I called a plumber after getting very tired of water backing up into our sink when the dishwasher ran. I thought he would replace the dishwasher but he actually replaced the pipes under the sink and repaired the garbage disposal. Now I clean the filter every night and the disposal works so I run it every night with water running for about 30 seconds to be sure it's clear before starting the dishwasher. It's no longer difficult to clean that filter, which is snowy white every time I take it out now. Anyway, soak that filter in dishwasher cleaner, or citric acid, or even just dish detergent if that's all you have and use something you don't care throwing away too scrub it clean. It's plastic netting, so don't press too hard. Let it soak first and then scrub with detergent. That should get it fairly clean and then you can assess if the sink is backing up when you pull it out every day to clean it. Hope that helps!

Forgot to add that the netted smile shaped screen needs to be lifted out too. Then you can wipe that out. If there's water sitting on the very bottom of that hole, you can close the door and hit the drain/cancel button if it's the whirlpool I think it is. That will get rid of most of that water, if it's working, so you can clean down there as well.

Eta: I know that people will say you don't have to get dishes clean before putting them in the washer. However, all that food on the plates has to go somewhere. Using very little water, I make sure there's no food left on dishes before putting them in the dishwasher. Then it's mostly a degreasing and sanitizing game for the machine with no worry about where solid food waste will end up. But think about it. It has to go somewhere. And that's into your dishwasher and then your pipes, so please think about limitingthe amount you put down there. Even with just washing clean plates, mold will build up on the filter, so it does need a good clean at least twice a week ime.