I'd suspect that Microsoft probably is not involved, at least not in any remotely direct way.
Microsoft is busy trying to broaden adoption of its Google competitor products, such as Edge and Bing, and it really does not need the PR headache that would ensue if it was tied to this pretty seedy anti-Google group. I mean, Microsoft still has its past anti-competitiveness practices hanging over its head, and the broader public still regards Microsoft with a tinge of cynical skepticism. Were Microsoft to involve itself with Oracle's dirt-digging operation, and that involvement was known, it'd probably do a lot to bolster anti-Microsoft sentiments, and further hinder Microsoft adoption where alternatives (especially Google's) exist. So, yeah, it'd probably be best if Microsoft steers well clear of this thing, and I'm sure they know that.
That said, Microsoft definitely has an interest in Oracle finding success here, so they'll probably find some means of supporting this group, but very indirectly. I wouldn't be surprised if there's a lot of non-binding winking and nudging to get some of Microsoft's business partners on board.