I tried to do this about 10 years ago to deal with transitioning a company we had bought out, to "sync" two mutually incompatible pieces of software. The biggest issue is primarily the column types are so different in some cases, I had to write a custom piece of software to even deal with it. It was a nightmare.
I can tell you too that the MySQL Workbench tools for converting MSSQL data to MySQL/MariaDB don't work worth a damn unless your MSSQL schema is very simple and has no defaults. For some reason MySQL/MariaDB doesn't allow more than one current date for column default, but MSSQL does. So, if you've got a table with more than one of them, you're screwed for conversion, and that's just one example.
Now, going back the otherway is an even bigger nightmare, so if you're thinking of syncing back and forth, it is not going to happen.
After we got it working the primary project then our primary software just began inserting/updating directly into the MSSQL database and our MySQL databases, and reading only from MySQL. Of course, this meant anyone using old things which used the MSSQL data, it was effectively read-only, but that was fine for our situation. The next project became to just get rid of that old software completely to avoid MSSQL at all.
I'd setup a local MSSQL database and connect to that, and essentially slave it to the remote one, or master-master if you need to sync it both ways.
So, really, either use only MSSQL or only MySQL/MariaDB, seeing how you already seem to have MSSQL, I'd stick with it. You can find some pretty generic connectors out there too (as you mentioned) or just connect to the remote one. It's not worth it to try to do what you are trying.