What goes into this since you already recycle bio, cardboard, plastics and metal? My "generic trash" is a 25 liter bag that I empty about once a month or so. Since most things go to the specific recycling containers, the generic waste is dominantly just napkins and tissues that shouldn't go to bio.
I don't have kids so no diapers or anything like that, but 120l weekly sounds still a lot after recycling.
I have lots of kitchen waste, grass waste, and plenty of brown organic matter I can add that’s around my yard. The bugs love it.
Sounds like too much water content and/or not enough air for aerobic bacteria to get to work. Tossing the pile with a pitchfork somewhat frequently should help it.
Unfortunately, compositing when you live with wildlife is a challenge. I don't bother because if the raccoons didn't get into it, the bears would, and both are annoyingly messy when they do. I even had a bear do structure damage to my garage when she broke in to get at the garbage one year.
I’ll try again with more dry leaves. Spring is close to starting in my area.
Your local hardware store may also have some compost kickstarter liquids as well, which might be helpful if you want to get it going before too many flies or ants come out to infest the pile.
How large is your property? I can put the actual pile some distance away on a > 1 acre lot.
In the past, I composted cat litter (paper variety, not clay) in a compost pile, and that did cause serious odor problems. Don't do that.