Looks like the Push extension suite is perfect for this.
It adds similar features such as Upload, Download, and even Compare local and Remote file's. Please search for it from the VS Code extensions list.
You can also configure the different environments.
Here is the context menu when right-clicking on a file:
This is from author's page on GitHub
Features It currently provides:
Transfer of individual files. Transfer of folders. Queueing (and
transfer after save bulk). Watching of files within the project. SFTP
gateway support - connect via an SSH gateway/bastion to your SFTP
server. ⚡️ Quick setup Push supports many options and configuration
modes. The most common of which is a single SFTP setup for an active
workspace. The following steps will help you get set up in no time:
Install Push from the [VS Code extension marketplace][3]. In the command
palette, choose Create/Edit Push configuration and confirm the
location (usually your workspace root), then choose the SFTP template.
Fill in the missing details within the settings file. At minimum, you
will need a host, username, a password if not using keys, and the root
path which will contain the workspace files, starting at the root
defined by the location of the push.settings.jsonc file. You should
then be able to upload files within the workspace by using the
explorer menu, title bars, or command palette. For more complete setup
and configuration details, feel free to read on.