I also lived in Munich for a while and still know people there who have either just built or are still looking. The prices there simply make no fun at all, even with your really good incomes. From my limited experience as an observer, in markets with almost no supply, there are often step-like increases but no price drops. At some point, hardly anyone can pay the high asking prices, and then they stagnate for a while. When people then earn a bit more again or larger loans are possible due to low interest rates, the next price round continues.
A former colleague with a similar income to yours recently wanted to buy a large city apartment for 900k. I told him he was crazy to spend that much. He was outbid and is now looking for single-family homes around 1200k. However, in the southeast of Munich, which is probably even more expensive.
I am very glad to be away from the area and to have found something affordable here just before the currently ongoing really big increase.
Good luck
Michael