Make the only satellite internet and monitor the traffic while holding the keys to internet access.

Sell autonomous cars with internet access and remote controls.

Gatekeep access to space travel.

At this point, you can monitor all of society secretly, use that information for propaganda, stocks, mergers, idea theft, blackmail, sanctions, etc., or cause mass disarray with your army of remote controlled cars. I don’t really know what the ai would want or do at this point, but I do know it’s a lot of power.