How to extend my kitchen counter to a breakfast counter?

Under the granite ledge add a counter top of wood. It could hinge allowing you to drop it down when not needed. You could also have the side come down with the same wood creating the waterfall look. You will need shorter stools.

Or get a narrow high table that can fit under the counter ledge that can expand when needed for company.

https://www.diynetwork.com/how-to/rooms-and-spaces/kitchen/how-to-create-a-raised-bar-in-your-kitchen

https://www.youtube.com/watch?v=DDsCRTiJuWE

https://www.pinterest.com/pin/317363104973665038/

Decide on the width the table-top needs to be and cut a sturdy piece of plywood to size. If you don't need rounded corners, all the better! Next, decide on the the surface. You can use just about anything for the surface from wood veneer to Formica to epoxy paint (or food-safe paint) to tile - even laminate flooring might work. Also, decide on how you want the edges finished. You can always just cut a strip of wood or molding and attach it if that's easiest. Next, find the studs inside the sink cabinets and secure the table top to the base with corbels (or corner blocks). You'll probably want four if you're doing the entire length. The stools may be a bit high, as Barb has noted, but you can't really determine that until you're done.

Would something like this work for you?

https://www.diynetwork.com/blog-cabin/2015/kitchen-pictures-from-diy-network-blog-cabin-2015-pictures?im=4

here are numerous folding desks--you could use this basic idea lower cost than construction https://www.youtube.com/results?search_query=DIY+folding+desk

You can add a piece of approximately 1 inch piece thick of plywood just underneath the present edge. Purchase nice fancy block pieces, available at your hardware store and place them at intervals, at least every 4 feet, along the underside of the plywood. Be sure to screw the end blocks into any strong cabinet boards that may be available to use. If not, put an extra piece, 1X2 or 2X2, inside the cabinet wherever you can as not to interfere with the operation of your shelves or drawers, to screw onto to make the counter top sturdy. Decide what you want to put on the surface of your addition and be sure to purchase the edging strip to match. Finish the additional piece before attaching it to the blocks. You will have a bit of an edge but that should be okay. This way your present granite will stay intact and it will be far less work to do the addition. You can cover the addition with granite or make it contrasting.

Anything you do at the current counter top level is going to look like an after-thought.

I'd go up. Get a really nice piece of wood that about 12" wide and finish it so it adds sparkle to the kitchen. Then you can mount it over the top of the counter top so it sticks out enough for eating. You would have to drill holes in the granite top which is no big deal.

You can make the top with its supports and mount it with a few anchors in the granite.

Just my idea.

https://www.homedepot.com/p/Bosch-1-2-in-Carbide-Tipped-Drill-Bit-for-Drilling-Natural-Stone-Granite-Slate-Ceramic-and-Glass-Tiles-NS600/301426412

My thoughts are to mount this about 6" above the present counter top so you would need some nice brackets to do so.