It's hard to see the "cobweb" from the photo though I do see something white.
But from other clues, I think the soil medium is too moisture holding -- I see lots of peat or coco coir but nothing to aid drainage and drying of the medium such as perlite or sand. In particular, thyme prefers better draining mix and I would have mixed 1/4 to 1/3 sand, even though basil (I think?) that is also in the same container could probably manage in here. At the very least, the soil medium need to be allowed to dry a little more before watering.
Also, these seedlings are too pale and stretching for light -- they need stronger light, and they are too crowded together -- they need to be thinned.
What kind of lighting do they get? They may still be salvageable if you thin them (clip off extras with small pointed like embroidery or cuticle scissors) and gently add a layer of sand and potting medium mixed together (1/3 sand) on top to bury the excess hypocotyl (stem between seed and seed leaves... DON'T bury the leaves), then provide more light. Putting a fan on them -- oscillating or personal fan to make the stems sturdier would be a good idea too though not strictly necessary and other ways can be explored.
As soon as they are sturdy enough, they should be separated since basil and thyme require different growing conditions.
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