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I am extremely rusty here, but I think you should probably read that as confirmation that even in a worst-case scenario, the image on the left-hand page won't be visible at all on the left edge of the right-hand page.
One factor that comes into play is that the effective gutter in a bound book varies a bit between different pages, aside from normal variance in trimming. Depending on where the page is in each 'booklet' of maybe 16pp, which is a folded and cut single print sheet, the spine will open up a little more or less. But the printer should look after all that, and should alert you if anything in your artwork might cause problems.
So what's really confusing me, is that when it goes into the preview on the printers' website, it looks like this:
The left page with a strip of the right, and vice versa. They'll both be lost in the gutter it looks like, so I'm not that arsed tbh. It's a mystery to me.