I haven't heard much recently from their more standard wireless attempts (other than Loom being used in Puerto Rico) but they did invest (jointly with Fidelity) $1 billion into SpaceX. The assumption is the SpaceX investments are specifically to support the SpaceX Starlink constellation which if successful could bring wireless internet to pretty much all of the planet.
1) It would help break up local ISP monopolies. Yes, internet is a bit of a natural monopoly, but if we can't have NN then lets start breaking ground for new fiber,
2) Google will need to lobby for changes in local regulations that prohibit local ISPs... which helps the local ISP startup market.
Google won't do that because of its political ties. To open up local ISP competition, you need to get rid of things like build-out requirements, loosen permitting requirements, reduce the ways people can stall installation of Fiber huts for NIMBY reasons, etc. Google will happily push for waivers of those requirements (as it did in every Fiber city), but cannot politically justify lobbying to eliminate those requirements for everyone else.