VS Code Deploying User Interface similar to MavensMate?
There isn't such a feature in the core bundle, nor does there need to be. VS Code handles multiple orgs without any problems, it's just different. You don't need to select individual files, because you can have as many folders as you need to organize your metadata. You no longer have a single src/classes folder, you can instead have core/classes, marketing/classes, and test/classes (or however you decide to organize your code structure). Once organized, you can easily deploy a single subset by right-clicking and deploying a folder. You can also deploy individual files if you'd like, but I find this to be less useful in daily tasks. That said, VS Code has a pretty robust extension system. It'd be possible for an enthusiast to build their own UI and even share it with others in the VS Code Extension Marketplace. If there's enough demand, it likely will be built by someone at some point. See also questions on here like this one for more information on folder structures in SFDX/VS Code.
Something that is related, but not exactly the same as how MavensMate allowed you to deploy Metadata is the VSCode Org Browser.
- Open Org Browser
- Refresh available metadata types in the org
- Default org
- Metadata type
- Metadata component
- Refresh components for metadata type
- Retrieve source for metadata component
It is currently in Beta and only supports retrieving metadata from non-scratch orgs.
You would still need a separate mechanism to deploy source metadata to another org.
You could raise a feature request to allow it to deploy selected metadata.
UPDATE: See Package.xml Utilities
Deploy Working Set - Deploys all the items in this working set to the currently selected org.