I went through all the Meguiar's products and it seems like "Ultimate Compound" then "Ultimate Polish" is what I want

Did you actually try those, or is that just looking at the ad copy for the different products? There are a lot of different products out there. My guess is that many are thought up in the marketing department. Basically, it's just a matter of different grits of abrasive, though some of the higher-tech products like Liquid Ice (Norton) and Finesse-It (3M) actually break down to finer grits as they are worked.
I think some of the 'Ultimate' products may be too fine to do the initial job for you, but there's no harm in trying them....I have a (small) shelf full of different rubbing and polishing compounds from my hobbies (luthier stuff as well as the fiberglass and paint jobs).

the next step for auto carbon fiber is to apply "Liquid Wax".

I probably wouldn't bother with wax, but if you do apply wax, try to use a product that doesn't have silicones - they will interfere with any repairs or refinish you might have to do in the future. Rattle can clear spray would be a better bet.

Maybe I'll just get it shiny and new and leave out the waxing step...

That would be my approach, probably.
I know paddles are expensive. I try not to abuse mine, but it is a tool, so I don't get too concerned about scratches. But if I saw the whole surface getting hazy, I'd look at shining it up a bit. (..if it didn't have the big white paint stripes on the blades.. :-) )
BTW a lot of us stick SOLAS refective tape on the paddle blades. Anything except waving those 'invisible' black blades in the air.
'White' or other bright colour blades are useful if trying to locate a swimmer (with waving paddle) in the water and very useful if using the paddle to signal folks when doing surf landings. (Experienced paddler on shore, signalling go-wait with paddle.)