Like T systems.
As a reference, most of those companies will pay engineers according to the IG Metall Tarif, which can e.g. be found there: https://www.igmetall.de/docs_MuE_ERA_Entgelte_Juni2018_78d3e...
This is per month, and there's 13.26 monthly salaries per year.
Engineers will typically not receive the highest lines which are reserved for managers, but something below (e.g. EG15 in Baden-Württemberg).
There are some company specific and performance bonuses on top of that, which might be up to 30%, but are typically far less (and often not performance but age-based). In the end things top out far below 100kEur for most engineers there, with no chances to get higher without moving into people management.
I worked at one of those companies (not the listed ones, but a similar one) for a couple of years, and found these things pretty frustrating after a few years.
Technically there existed individual contributor levels on that level. However they were only given to senior managers who failed at their job of leading people, instead of ICs that had been really good at what they were doing.
Virtually every "How much do you earn?" thread that pops up on HN has loads of comments with Europeans being surprised at the amount of money Americans make in tech.
Further - right now America is close to uncontested in the amount of technology it is producing and exporting. The only widely used European software I can think of is SAP. America is winning the talent war. I've only had a few friends who moved from US to Europe for tech work - and in all cases it had nothing to do with the job. Had more to do with wanting to "explore new places". On the other hand, I know tonnes of Euros, Indians, and Chinese who have come to US to work.
That you personally only know few people who moved to Europe from the US but many who moved to the US probably says more about your location than about general trends. I know only few Germans who moved to the US for work, but many Americans, Iranians and Chinese who moved to Berlin. But that's where I live, so it's to be expected.
I would expect BMW to struggle the most among the German giants, if Tesla doesn't stop growing soon. The rise of Mercedes back to top form was a bad enough of a hit for BMW, then Tesla comes along poised to sell $40 billion worth of cars every year in the near future (all of which cost far more than ~$35k, which is a direct shot at all the luxury makers).
Germany is sitting in a great position nationally (epic trade surplus, good national finances, and reasonably fine household finances), now is the time to aggressively invest if you're them, to try to build out a large number of new technology jobs.
Most dev salaries at local companies are garbage compared to what FAANG companies pay in their EU offices.