For what you're describing there isn't really a single tool, nor would you probably want one. What you want is a Code Review tool for the portion that reviews the code, a CI (continuous integration) tool or tools that handle validation, test builds, static analysis, code metrics, artifact generation, etc, a tool that controls what goes into your repository, and a tool that brings all these results together. In some cases one tool might provide multiple of these, while in others you might only get one of these features.
Common solutions have things like PerforceHelix, GitHub (cloud or locally hosted), GitLab (cloud or locally hosted), RhodeCode, etc as the central tool that handles the repository(ies) management and the results collection point. You then either install other tools that integrate with them or provide plugins to them to accomplish the additonal tasks like code review and CI.
For my company we have somewhat similar needs/goals. We have a self-hosted GitLab instance, then choose to integrate it with SmartBear Collaborator for rigorous code reviews, and Jenkins for our CI. With GitLab Enterprise (paid, but mostly open source) you have change gates called Merge Requests (they're called Pull Requests in GitHub parlance) that require approvals to merge into the master branch of your repo(s), and these can be dependent on the Enterprise-only "Pipelines". Pipelines, along with Runners are designed to implement your CI build steps and ensure test builds succeed, unit tests pass, etc. They're setup so you can have multiple steps in your Pipelines, so if you need to generate static analysis results and post a link to them for review, you can do so. Keep in mind that every single person has a different need in this area, so they provide the building blocks and it's up to you to stitch them together with yaml files and Web hook/API scripts to/from other tools.
If you have need of a rigorous review process, and want to be able to include changes across multiple repositories, one of the only tools I've found that does it well is SmartBear's Collaborator tool. There's a user-count-limited free version you can try out, and they have regular free Webcasts you can join to see how it works and ask questions about it (of a real and knowledgeable person). The code itself is unfortunately closed source, and beyond 10 users you have to pay for licenses, but they have integration support with GitLab (self and cloud hosted) and GitHub (cloud hosted only), as well as a couple other options I haven't looked too closely at.
Smartbear Code Collaborator
Customizable independent workflows (templates) specifying:
- How many members of each role of up to 4 roles must be on a review.
- Whether a role in the workflow is required to approve changes, optionally can, or doesn't approve at all
- How many of a given role must approve the review (includes all, none, or a fixed number)
- Unique names of the roles
- Fields (drop downs, multi-selection, multi-line text) and field requirements (regex, length limits) for reviews
- Bug/Defect fields
- Whether a post-approval E-Sign step is required by all members of one of the roles or not.
It keeps a running audit log of all actions by all users on all reviews that is mostly unmodifiable.
By directly uploading changes to it, you can have as many different repositories in a single review as you'd like, and all the repositories can be automatically identified (git repositories at least).
It's one of the few tools that does a good job of reviews on MSWord/OpenOffice/LibreOffice documents, and has a decent way to comment on both the documents and image file comparisons (floating pins).
(screenshot from unknown Google Image search results)