Hi Hannes,
Have a look at the related question with answers here?: https://forum.mendix.com/link/questions/110360
there are well written accepted answers to this. You probably already found the documentation: https://docs.mendix.com/appstore/modules/data-grid-2/#8-configuration
There are two things you can save:
1) The column configuration (hidden, sort, place)
This is done in the genral Grid2 setup under personalization. As you already did.
It is stored in a unlimited string.
2) The filter settings per column.
These must be set in the filter itself. So double click on the filter and see the personalization.
You need a unique attribute per column, in the same entity as used for the general personalization.
The attribute should fit the type of the column attribute. So column shows a number, then the attribute to save the personalization should also be a number (use decimal, also for integer). Enumeration must be a string.
Just try it out. The drop down in the personalization shows only allowed attributes.
BTW; I create a bunch of attributes in the “saving entity”. String1, String2… no real need to name the attributes related to the attributes in THAT Grid. So you can use the same attributes in any other Grid.