Is this somehow tax related? Or does it give the EU power over those companies in a way?
It's got benefits in terms of bringing in tax money, both directly from the companies and indirectly from their employees.
If you're known as a top location for a given service, it can also make companies want to open up there, if they want to attract talent from their competitors (although this may change as more companies move to remote-first employment)
Sanctions preventing Iran from working in USD or accessing Western banks have been 100 times more effective than sanctions on weapons or oil at bringing them to the negotiating table. That's why you don't want to rely on foreign Financial Services...
There is tax revenue, jobs and the ability to sanction others. But it's the reliance on something you cannot control angle that makes this a MUST issue instead of a Would Be Nice issue.
You'll get some level of capital gains from profits, along with any corporation taxes.
But crucially you get control over what gets credit and what rules are attached to it.
the EU doesn't really have a banking union, which means that rules money markets are country dependent. As long as london was the EU trading centre, then there would be no banking union, as it would cause london to loose money.
Yes.
New York law is dominant in finance because New York City is a financial nerve centre. This gives high-tax paying persons like bankers and lawyers and investors an incentive for being nearby.
In the New York courts, there's a much longer history of relevant cases decided, judges with more specialist knowledge and the system is used to the workload of large and complex cases. This all combines to give a perceived higher degree of predictability.
The other replies to this are interesting though and it's not all one thing, distributed decision making can be rationalized after the fact any number of ways
Having top stock markets (and commodities markets) accelerates local economies and makes the city/country more important globally. See NYC, Tokyo, Hong Kong, Singapore, Shanghai and in fact even London.
The more the listed companies you have, the more of all of the above jobs.