Short answer: go to the hardware store, buy whatever, paint it down and watch it fail in a few years. What you do at that point depends on what you used.
Or you could consider over-roofing it with EPDM rubber, using the rubber-cement-like glue to stick it down (paint both surfaces and join them). The easy made-for-wood glue won't work. Careful pricing this solution, the rubber is cheap enough, the cost is in the adhesives.
Long answer: you're not going to like it.
Galvanized steel is quite a good roof, until it's not. Then you want to deal with it swiftly. You have a roof which is also shaped to provide a roof drain not on the edge. Hard to replicate.
NASA has a lot of steel structures. They throw serious money into corrosion research, and they have a web site just for that.
I spent hours reading it, and sure enough, their advice conforms to my experience fighting the same fights. To summarize:
Your choice of paint is not as important as your surface prep.
That said, better paint is better.
Chemical rust "converters" don't do much.
Out of heavy disc sanding, abrasive-disc grinding, needle scaling and media blast, media blast to near-white metal (SSPC.SP10) wins, needle scaling is a distant second, and the others aren't even worth the trouble.
For removing rust, I decide how serious I am. Either I'm willing to break out the gear and do full-on media blast to SSPC.SP10... or I'm not. If I'm not, then I do what I can with hand wirebrushing and palm sanders, heat it over 212F with a hair dryer (to remove all water), wipedown, and then... umm... I haven't found much that works. To my surprise, West System epoxy used as a paint has held up 3 years so far. I used it because I was using fiberglass mat to bridge some holes. However, it needs to be primed and topcoated, because epoxy by itself is vulnerable to UV light and will turn to swiss cheese. I am also experimenting with plain ole Rustoleum 7769 rusty metal primer, then a much better primer and paint, just to see if it'll perform as advertised. I haven't actually tried cold galvanizing compound over rusty metal. Remember, this is a difficult problem to solve, with no good answers.
Cold galvanizing compound is basically paint, but with 90% zinc instead of the usual fillers and colorants. The can is so heavy that a gallon will break a gallon paint shaker, and it must be agitated a lot or the zinc will fall to the bottom of the can/cup. Zinc is what actual galvanizing is. After a year or two it weathers to look a lot like real galvanizing.
West System is wonderful stuff to have in your home workshop with 100 uses. Bit of an up-front cost but you'll never buy epoxy or bondo again, and you can now do fiberglass layup.
If I am serious enough to media blast, then I would lay several layers of masking tape (or duct tape over masking tape) to protect seams I didn't want to damage. Blast, wipedown with solvent, and paint either the cold galvanizing compound and done... or if possible zinc-chromate primer (Rustoleum even makes one, in the 7400 line)... followed by the proper primer for my topcoat of choice. I would expect 10-30 years out of that, depending on the quality of the topcoat, and if it's caught early, unlimited extensions simply by repainting.
Now as far as elastomeric rubber coatings or plain old "tar", it will gap you for a year or three. When it starts to leak/fail, you can do it again 1-2 more times. After that, 3-9 years out, it becomes too thick to seal - with cracks and separations being too big for further coats to bridge across. Now, your options are unpleasant. You can painstakingly scrape the stuff off, but I find it not worth it. Or, you can remove the roof and start over at that point. So tar-like roof coatings are a dead-end solution.
If you own this house, resale value is a factor. A cheesy repair will be caught by a homebuyer's inspector, and he will tell them to price a roof replacement into their offer.