Generally speaking it sounds like you want to be in control of the deployment steps, so pushing changes from development to staging to production; or whatever your exact process is. So you give your developer only access to the development environment for example, but there you want to keep an overview on all the changes made. In my mind there is no need to use plugins for the version control.
git diff should be enough to keep track of file changes, it does
Show changes between the working tree and the index or a tree, changes between the index and a tree, changes between two trees, changes between two blob objects, or changes between two files on disk.
Show differences between commits:
git diff old new
// file names only
git diff old new --name-only
For more options please consult the documentation.
I think this is fairly obvious, and pretty much only a matter of monitoring changes.
Regarding the database, you can use
mysqldump to get your database into a file
The mysqldump client utility performs logical backups, producing a set of SQL statements that can be executed to reproduce the original database object definitions and table data. It dumps one or more MySQL databases for backup or transfer to another SQL server.
mysqldump --skip-extended-insert --skip-comments -u username -p dbname > dump.sql
The command can be specified to exclude certain tables, e.g. you don't care about the
wp_posts table in development, or you only include specific tables, e.g. are there changes to
wp_users – in short, greater exactness can be achieved.
And then you use
Compare FILES line by line.
diff old.sql new.sql
And check for differences, and see the changes that have been made.
Of course the database backups/dumps can be automated, and e.g. version controlled too, but I'm not getting further into that.
After the checks, if all the changes made are wanted and production-ready, you can implement your deployment strategy.
I feel like this is a reasonably simple process that could be implemented to achieve the control you want.
Aside from that I wanted to outline and illustrate a process not depending on plugins.