It’s not the garden they raid, it’s the kitchen.
I’ve learned to clear away the cat’s plate at night so I don’t find it gossamered with slugslobber in the morning. Sometimes with Silbo Sluggins the quiet burglar still in the dish.
There’s a technique for getting rid of them humanely, I call it the slug-flick. (“Where do you go to my slugly?”) Fold a paper kitchen towel in four, pick up the slug without (ugh) touching it, roll it left and right so it curls up and stops trying to stick to the paper, then with a flick of the wrist it’s off down the garden (“I believe I can fly”) sometimes with a splat as it hits a wall but it never kills them.
They keep coming back, they know the way; does one of them act as a scout on the Chisholm Trail to our back door? Caught four the other night, different sizes, from grand master to apprentice.
I think Vivians comment points towards finding their source and then having identified it and if its possible, lay some Diatomaceous earth and the slugs wont crawl over it. It is harmless and inert but its composition means it is difficult for some insects to cross. I find I can tolerate snails (not in the house) but not slugs and yet slugs are an important part of the chain and are food for hedgehogs, toads and thrushes to name but a few. Why do we find them so disgusting?
I feel for you - having liven in slug city central for decades. If your kitchen is in an extension with no second floor above it, then be aware that some of the slugs raiding your cat's bowl may actually not come from the garden but live in the roof space.
In any case, there's no way to eradicate slugs totally unless you want to drench plants and soil with chemical 'slug-death', thus also affecting other animals living in the soil or living off slugs ...