The features you are talking about, like having a search engine, are in just about every product that could exist in this arena. Have you used GitLab and GitHub before for issue and project tracking? What about Phabricator?
Most start from scratch projects can be nicely managed in Trello et al.
Generic search alone isn't the feature, or the benefit. None of those options listed have a deep enough search. GitLab and GitHub aren't a project manager - projects that are manageable in Git* likely aren't complex, or enterprise grade.
I have tried nearly every product in this arena as well over 20 yrs of dev in different types and sizes of projects. JIRA begrudgingly is my neccesary evil. I hear nice things about Pivotal Tracker as well, just didn't reach my sphere of folks when I was looking.