Since tag support is already a core feature of Obsidian, I would argue this feature request is best implemented as a core feature. As @WahWah said, this is pretty standard in apps that support tagging.
As to the specific UI implementation, @malecjan mentions several good options. As with other file management actions, I think it makes sense to let the user do it in several different ways. Using the File Explorer and Search Results seem to be the most compatible with Obsidian’s current UX.
File Explorer
First, multi-select of files in File Explorer, then
→ right-click menu “Add tag to selected files”
→ command palette “Add tag to selected files”
→ drag selected files to the tag in the tag pane OR drag the tag from tag pane to the selected files
Search Results
First, perform a search query that give results, then
→ click a new # button (next to the ‘copy search results’ button) to assign a tag to all notes in the search results