There’s invasive species, naturalized, non-invasive, right? So any species that’s on an invasive species list for an area is already a no go.
Naturalized, like, arguably stuff like dandelion is, and its not causing issues (outside of a few areas) because all it really does is grow in turf grass or disturbed flower beds.
So that leaves stuff that isn’t invasive and doesn’t naturalise itsself - I feel like this is the area of plants that I feel like its generally the things that are going to be okay to plant even if they’re not native, but they don’t really get talked about (outside, ooh, that’s pretty, when you’re at a garden center,) because they’re just… not causing issues. An example that comes to mind are the various hybrid barrenwort species you can find for sale at garden centers; I have a few myself, they’re nice for the shade and I don’t think I ever even see them pollinated.
Or columbine hybrids - sure the hybrids will drop seeds and root but they’re not really vigourous enough to crowd other things out, and the (also not native) columbine sawflies will do a great job of keeping them check in the spring while for some reason leaving our native Aquilegia canadensis alone.
I’d consider a pretty garden plant that doesn’t really get aggressive and might actually get your typical midwestern homeowner to plant something besides boxwoods and hostas a bonus.