Like they are direct competitors no?

No, Google pays Firefox to make it seem like it still has competitors and isn't a monopoly. However, a key condition of that payment is that the default search engine in Firefox is Google. They change that, they lose most of their funding -- not most of their Google funding, most of their revenue (which is nearly all Google).

Wouldn’t Mozilla be motivated to fuck google as hard as possible?

If they still existed as an actual company, sure. But, it's not. It's a corpse that Google animates with their huge funding to make it seem like they still have competitors. Technically, Google doesn't own Mozilla, but in a 2012 report, 85% of their funding came from Google. So, they're never going to do anything that risks that funding.