CO2 and water for full combustion. Since rockets run fuel-rich, also some CO, H2, and a little elemental carbon...the methane itself decomposes at high temperatures. There's also a little bit of nitrogen oxides produced when the hot exhaust mixes with the air.

Hydrolox rockets technically don't produce CO2, but producing the hydrogen does. And while you could technically produce carbon-neutral hydrogen, you could also use that hydrogen with captured CO2 to make carbon neutral methane, and the latter's much less energy intensive to store and will have far lower losses due to leakage. Plus, hydrogen-burning rockets usually need solid boosters to get off the ground, and those put out all sorts of noxious stuff, including lots of carbon and lots of hydrogen chloride.

You have to keep the scale in mind though. Even a Starship launch only uses about a thousand tons of methane (most of its propellant by mass is liquid oxygen). Global consumption in 2021 was about 8 billion tons per day, just losses to leakage were several hundred thousand tons per day. All rocket launches together are in the rounding error of total emissions. In short, any effort spent on them is wasted, no matter how effective it is...you could eliminate rocket emissions entirely and make no difference globally.