What data does the ECU store?

The ECU operates the engine and stores any faults it sees along the way.
Every time a Lane light comes on Steady or flashing,  an Entry will be made to the Error log file.
At least once a year YOU or your mechanic will use the BUDS software to download the ECU Data and Review and Clear the Error Log File.
Most entries will be expected intermittent events.
e.g., A Lane test will produce a Lane Fault as expected.

It is expected that you will personally own or have access to the BUDS Software and Dongle.

The Data is stored indefinitely until cleared.
This does not involve the Rotax Factory.
It is an ECU - Engine Control Unit, Not a Flight Data Recorder.

So the higher level BUDS access can't be used to retrieve any more data than the version you can buy?

All levels read all the Data and Log files that are available.

Level #1 Viewer - is essentially a read Only device.
Level #2 Service - also allows the user to clear the faults so you don't have to keep looking at ancient faults after repairs.
Level #3 Maintenance - also allows some minor parameters to be changed and the ECU to be Updated.

See pages 2 and 3 of the Service Instruction for a summary of the function available at each level.

But "Fuel and Ignition" is only available for level 2 and above, and "Internal and GSM" and "Turbo" are only available for level 3. So not all data?

What kind of data is in there? What does GSM mean anyway?

GSM = Generator Select Manager.

Based on Current Pricing, There is no reason to not just go with the Level #3 version.