We use a high-end Miele dishwasher, model 6875. It's amazing (though expensive) and it's the only dishwasher I've had that I didn't kind of hate, and it has lasted perfectly for several years now.

Miele Model 6875 (now discontinued):

https://www.designerappliances.com/miele-g6875scvisf.html

We don't use it for knives, pots, or non-dishwasher-safe items. For those items, I wash them by hand. For years I have used this scrubbing cloth:

Crown Choice All-Purpose Cleaning Scrubber

https://www.amazon.com/dp/B07YP16LK9?psc=1&ref=ppx_yo2ov_dt_...

That scrubbing cloth is great because it dries out quickly, never gets smelly, does not scratch anything even if you scrub hard, and lasts a very long time (at least 6 months of daily use, but probably a year or more).

For gummy stuff, I usually use a dish brush before the cloth to knock the gunk off of the dish so that I don't have to later clean it off of the cloth. I've never found one that I like well enough, so I won't post a link.

For stuck-on stuff, I use a Progressive scraper:

https://www.amazon.com/Progressive-GT-3300-Gadget-Scrapers-D...

Those are sold out, but these look similar:

https://www.amazon.com/Multicolor-Silicone-Dishwashing-Multi...