Hear, hear. I am formerly Google Payments too. Don't leave just yet, there's plenty of hope for you staying and transferring to another org.
I have been at Google about 12 years now and had a three year stint in Payments until somewhat recently. Out of all of the organizations, projects, and products I worked on (6 projects, 12 managers, 5 offices, 2 continents), Payments is the least Google-feeling of them all with the worst management and politics (frankly it was fucked). The rest of Google was a dream in comparison. Had I known Payments was in bad shape, I might not have joined it originally.
Before leaving, try somewhere else. I recently founded my own team elsewhere build software for distributed system infrastructure, and I cannot tell you how fun it is. The joy is still at Google, but Payments is a blackhole. I can't believe the rest of the leadership tolerates that hostile black sheep of an org.
I think financially it might best to stick at Google but change jobs. However, since you mentioned Space-X, remember that your skills set is not the core of their technology so you would not be able to get into one of the critical teams immediately. But sometimes you can make multiple jumps in position with time till you get closer to what you desire. Use your friends and former coworkers to help you lead into new opportunities. I look at what I did 20 years ago and it is quite different that what I'm doing now. And there were many job transitions over that time to get there.
I am (I suspect) a little bit older than you and have been working at a FANG company for nearly seven years. (Before that I was at a company that may as well be included in the list.)
What your comments about aerospace remind me of is something I would myself frequently do: fantasizing about a different industry about which I know very little. (Years ago, I used to imagine going back to school to study law, on the grounds that being a lawyer is a good way to really work for social change.)
Obviously I didn't go back to school, and I certainly can't tell you what the right decision for you is. I think a bit of curiosity about the road not taken is natural--but you also have to be clear-eyed about what the alternatives actually look like.
To your specific question, however, I would strongly recommend interviewing at a few other teams inside the company and a few other companies. Before I came to my current employer, I interviewed here and a few other places. Some of them struck me by how _bad_ the interviewers were; in fact, my interview experience at my current employer (where the interviewers impressed me by their intelligence) convinced me, at the time, that if I didn't get the job I would stay at my then-employer rather than move to a less impressive place.
So interviewing can be clarifying in terms of showing you what else is out there, and helping you make a trade-off between natural wanderlust and, you know, not settling for something shitty just because it's new. ;)