Great question — answering as the UphillTech team:
This looks fine for a first coat. As long as it's not wavy, you're fine. The only mistake I can see in the picture is that you may not have done a good job of trimming the paper around the holes in the drywall; they need to be completely flat. You need at least three coats to patch drywall. I've always seen the fiberglass mesh (or the paper tape) through the first coat. The compound shrinks a little when it dries. I would not remove the fiberglass tape unless you have excessive compound under the tape. The fiberglass tape is a thinner patch than a paper tape, because with paper, you need to put compound underneath and over the tape. I would just apply another coat, expanding the area coated...
Full answer by Edwin: https://diy.stackexchange.com/a/330673 (CC BY-SA 4.0).
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