Dear Maraika,

There is a good chance that your hosta were eaten by deer, as it is a favorite food of theirs.  Here is a pretty good list of all that might affect hostas, which includes deer of course.:

Hosta Pests and Diseases - Gardening in Michigan

It looks like from the picture that the residual roots have invited some sort of mushroom  (fungi) into your bed. It looks a lot like turkey tail mushroom (though I am not 100% sure). Here is some information on them:

Turkey Tail Fungus - Katharine Ordway Natural History Study Area - Macalester College

The fungi is working to decompose the leftover roots from the honeysuckle. If possible, you may want to dig out some of the roots and add some additional composted manure or compost or soil to replace roots removed. At best, the roots are taking up space for good food and nutrients for your hostas. At worst, there may be some alleopathic relationship that would harm the hostas. I did find one article that talked about the ecological effects of honeysuckle which you may wish to read here:

Ecological Effects of Amur Honeysuckle Infestations - Kentucky Native Plant Society

For best and healthiest plants, knowing your soil is key. You may wish to do a soil test to check your soil ph and major nutrients.

Please let me know if you need additional assistance. Happy gardening,