Follow-up to #1077...
It would be great if the respective fields for node_nid, user_uid, file_fid and taxonomy_term_tid would be able to do auto-complete search and offer pretty entity names to pick from instead of the numeric fields we are currently providing:

(form elements in the screenshot above edited for visibility)

We should also replace those "cryptic" names in the drop-down menu with pretty names too like "Content: Title", "User: Username" and "Taxonomy term: Name".
The value saved in config would still be the entity ID, we'd only show a "pretty", human-focused autocomplete to the end user, with available options to select from.
PS: while at it, also replace "Node: Type" with "Content: Type" in the spirit of not exposing the term "node" in the UI.
Recent comments
Worth mentioning as it was in zulip chat by @yorkshirepudding I just tested and the two work together without issue as long as you don't use the "Exclude comments from Content...
Search does not include comments
There is also Node Comments Search - this searches the node and all comments (default search is node and first page of comments) as part of the content search. Izzy's module above is a separate...
Search does not include comments
I have created a new module comment_search
Search does not include comments