I don't know if there's a direct quid pro quo relationship between the CEO of Mozilla and Google but I feel quite confident that Google absolutely influences the organization in ways beyond just the cash injection to make it rudderless, uncompetitive and shrinking as you say.
It could be as simple as ex-Google employees at lower levels than CEO who are paid by Google take positions at Mozilla, or more subtle things like guiding the direction of the organization through standards boards.
It would be really fascinating to look at the org charts of Mozilla past and present and try and build the network between people who worked at Google or Google related organizations before, during, and after their time at Mozilla.
Because you're absolutely right that the organization is so absolutely dysfunctional that it can't just be incompetence, it has to be absolute malice.