Having a # symbol in YAML is not valid.
To search for tags you should use this syntax in the core search plugin: tag:#tag1.
If you just use #tag in your search query you are searching for that exact string to show up.
The help page on aliases shows the all-on-one-line, surrounded by , comma-separated list again (same as key3 above).
I use that same comma-separated list surrounded by  for tags as well, to save vertical space on my screen.
tags: [tag1, tag2]
The version from Craig’s post, without the , also works for me.
The version from DeniseTodd’s post works for me for a single tag, or when I have my full list inside .
Combining the usage of Craig and DeniseTodd does NOT work for me. The local graph no longer recognizes any of the tags.
To summarize and show some additional combinations:
tags: [tag1, tag2] works and is one of the list syntaxes in the Obsidian help YAML page
The other list syntax puts each tag on a new line, following a -. See above. Based on the help vault, the lines can either be indented or not. No  needed.
tags: [#tag1, #tag2] DOES NOT WORK # is illegal in YAML.
tags: ["#tag1", "#tag2"] seems to work (quotes escape the illegal # symbol), example from DeniseTodd.
tags: tag1, tag2 seems to work, example from Craig. I think this is only because the set of characters allowed in tag names is limited.
tags: "#tag1", "#tag2" DOES NOT WORK. Cannot combine the examples from Craig and DeniseTodd.
tags: "tag1", "tag2" DOES NOT WORK. Cannot use Craig’s example with quotation marks.
tags: ["tag1", "tag2"] seems to work. Can quote your tags even if not escaping anything, but need the proper list syntax with .
tags: [tag1, "#tag2"] seems to work. Can mix quoted+escaped# and not quoted, if you use proper list syntax with . This seems like it might be confusing when you look at the note in the future, though!
tags: [ tag1, tag2 ] seems to work, not sensitive to extra space.
I’ll be sticking with tags: [tag1, tag2] since that list syntax is on the official Obsidian help page for YAML, but it is interesting to know about the other variants! I wonder if all the ones that work are supposed to work?