Failed to save modifications to the server. Fatal error encountered during data read..

Hi, MikeO 

I can't find the same issue. You can follow the steps to connect:

Power BI Connecting to a database: Connect the MYSQL database to Power BI to build Dashboards - YouTube

Make sure the credentials are correct and the account has permission to access.

Is your powerbi version up to date? 

Download Microsoft Power BI Desktop from Official Microsoft Download Center

Can you connect to other data in mysql database?

Did I answer your question ? Please mark my reply as solution. Thank you very much.
If not, please feel free to ask me.

Best Regards,
Community Support Team _ Janey

Yes, my PowerBi version is up-to-date and I can connect to other data in MySQL.

Hi, MikeO 

You can connect to other data in MYSQL, it shows that there should be no problem with powerbi and mysql. 

Have you considered the issue of data source permissions?

Try stripping it back to a single query and use power query to remove all columns apart from a single text column just to see if you can import anything.

Not ever tried directly in PowerBi but I have occassionally used MySQL in a linked server configuration with MS SQL Server and had issues dealing with date types. If a single text column works, add in more columns until it breaks and then come back and we'll expand on next steps.