Drywall – a proper way to tape a 6” round hole from can light

I know this isn't the answer you want to hear, but I don't think priming and painting will hide the tape.

Before you apply any more primer, I'd add another thicker coat of mud. Slather on the mud thick first - it doesn't have to be smooth. Then smooth it out by angling your 12" knife so it's almost parallel with the drywall as you drag it along the surface. You'll have to press fairly firmly in order to avoid air gaps appearing in the thick coat you're smoothing out.

You may have to get a feel for it. If you push too hard and can see the tape again, redo that section until you get it just right.

Wait for the thicker coat to dry, then sand the edges as smooth as you can get them. Very carefully/lightly sand over area covering the tape if you didn't get it quite smooth. You may need to do a second coat along both sides of the thicker coat to make it join the drywall surface smoothly.

I'm not aware of anything special for fire rating a joint in drywall, just use the same joint compound and tape you would use on the rest of your walls. Fire rated drywall will cut similar to normal drywall, but it will offer a lot more resistance because of the embedded fiberglass.

When sealing any gaps or cracks, they make special fire rated expanding foam and caulk. They tend to be orange in color. There's also fire rated insulation that can be used for any utility chases/bulkheads that connect to the ceiling.

For junction boxes, we've been required to box our in on common walls (2x4 above and below the junction and a piece of plywood behind everything) to ensure that any shorts in the electrical couldn't travel to another unit, but I doubt this would be a requirement for anyone in a single family home.