This one is exactly the same request as https://www.drupal.org/node/197486.
Having an indicator on the modules list page would remove a duplicate interface that lists all modules, and be a more intuitive place for site builders to find available update information. Additionally, having the indicator in a place site builders visit all the time might also encourage updating more often, creating more secure sites for all.
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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