I think CSU is overplaying their ( weak ) hand.
Merkel is going to tell them ciao
CSU operates in one state (Bavaria) and CDU in the other fifteen. CSU is, indeed, to the right of CDU. Think of Texas and the Republican Party of Texas being separate from the Republican Party in the rest of the U.S.
If Merkel were to disrespect CSU, it would spell trouble for her and CDU. Possibly CSU would organize nationwide and relegate CDU to minor party status.
CSU is currently in the absolute majority in Bavaria. It has ruled Bavaria either in absolute majority or as lead party in a coalition government continuously since the formation of the Federal Republic of Germany.
Reflecting the conservative orientation of CSU, Bavaria is considered to be an economic powerhouse.
Bavaria has the third highest GDP per capita of the states of Germany, following the city-states of Hamburg and Bremen. To make a valid comparison to Hamburg and Bremen, you’d want to compare Munich (only) to them, and GDP per capita in Munich is roughly similar to those two city-states. Among German cities, Munich is second only to Frankfort in GDP per capita.
Finally, I will mention that the unemployment rate in Bavaria is 3.8 percent, as compared to 6.8 percent nationwide; and, is tied for first among the states of Germany.
https://en.wikipedia.org/wiki/List_of_German_states_by_GDP
https://en.wikipedia.org/wiki/List_of_metropolitan_areas_in_the_European_Union_by_GDP