I second this very much - the tag search seems inconsistent and inconvenient.
Proposed solution:
I think the Front-matter should be excluded from normal text search (so I think this suggestion is related).
The Tags from the Frontmatter should be properly included in searches though. So if I just search for #exampletag it should list them. Right now it doesn’t at all… I have to specifically search tag:#exampletag or tag:exampletag.
I find the same when searching via file: … which IMO should include the aliases. As that seems to me the idea of aliases, right? Because there’s no way to just search for title: for example, to include the aliases.
That the graph view would include tags was also my default assumption - it seemed logical. But I’m not sure if it gets too complex.
Workaround
Frontmatter YAML can also be in quotation marks like this " #exampleTag", then it shows in at least the tags both searches.