Well, before diving into new use of power, it should be noted that much of the national regulatory and investigatory infrastructure is managed by NY state as a matter of them being host. So even considering non-controversial actions like actually investigating claims of rote illegal behavior, NYS has a lot more investigators and courts that are prepared to process those cases. It's just like Florida has more laws regarding theme parks, and Colorado has more laws involving skiing, and California has more laws involving movie making.
Texas just has less legal tools and employees ready. It's been evident for years that companies want to avoid scrutiny and make investigations harder. Moving to Texas is essentially "security through obscurity" where they're just hiding from legal apparatus. Similarly, there is a direct correlation between the number of IRS employees and the unpaid taxes found in audits of big companies.
Much of the regulatory power they're wielding is "benign" to the average American - more strict details on reporting and disclosures, ethics, etc. They require more years and documentation of income, strict accounting standards, etc. The big thing is that it brings most companies into NY state jurisdiction for unrelated-to-exchanges things that impact finances. Over time, they've just grown and fine-tuned the "industry" of maintaining these laws. Just like actual wall street has grown.
The NY vs Texas jurisdictions are relevant because different state governments (Texas) compete on being "business friendly" and take a very lax approach to actually enforcing and investigating laws, as a matter of policy. A big and familiar - but political - example is trump's court cases on (allegedly) defrauding banks by lying about his properties worth - cases like that happen all the time (to less politically involved people too) in NY but not in Texas.
As some specific examples, The laws on exchanges in NY are more strict, so most crypto exchanges can't operate there. There are also state taxes on stock transactions.
Many people have written a lot about DEI and ESG requirements in financial disclosures, which is controversial, but they're not actually state laws of NY. They came from the SEC.
The only strong political example of "newly wielding power" would be the growth in attacks against oil and gas companies in NY by claiming that they lied in their financial disclosures related to risks of their product (ie. climate change).
That was prosecution of a criminal who lived in New York for a crime committed in New York; I fail to see how it has any connection to the state regulating _companies_ who aren't based in New York but are listed in New York.
I'm not saying the prosecution was unmerited, just that SDNY has signaled that it will prosecute, as opposed to finding a reason to look the other way, as may be expectation of the connected elites. The DOJ for example is telling its lawyers to drop the corruption case against NY police chief Adams as well, for crimes committed in NY state that happen to be under federal jurisdiction [0].
Unclear what business of the DoJ's that is. But, again, this seems totally unrelated to regulation or prosecution of non-NY companies which are merely listed in New York.
Can you give some examples of how they used some power recently, that they didn't use before?