Notably, it was struck down by a California court as violating the California constitution.
> under what authority does the EU meddle in business like this?
According to https://ec.europa.eu/commission/presscorner/detail/en/ip_22_... the policy represents an agreement among the European Commission, European Council, and European Parliament, with the latter two still requiring a formal vote. And the EU mandate will actually be on member countries to pass enacting legislation within their jurisdiction.
Prudent policy or not, I don't think there's any way to spin this as an EU end-run around the democratic process or member state sovereignty.
And I don't think this policy applies to foreign corporations, only to companies incorporated in a member jurisdiction. (But I haven't read anything specifically mentioning the scope.)
However don't get the wrong idea that this was just decided by someone in Brussels and it's a directive now. This is just a draft for a potential directive. This has not been approved by the European Parliament or the European Council. [1] Long way to go still.
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[1] "Once Parliament and Council have formally approved the agreement" https://www.europarl.europa.eu/news/et/press-room/20220603IP...
So no authority needed. But it's an interesting legal question whether the EU could impose such a requirement (backed by fines, for example) on unwilling member states.
By the way, the directive's wording is actually gender-neutral, talking about an "under-represented sex". If a company has a board dominated by women, it becomes a quota for men.