You'll only have one shot at this repair and have to do it right, twice in a row. As such I see two "safe" options.
Send the frame to a bike shop or someone handy with tools who has done this before. You've not done this before and the risk is reasonable. There will be a cost naturally.
Leave it exactly as-is and ride the bike like normal, but without a kickstand. If you really need a kickstand, fit a different type that secures elsewhere to the frame. The two stubs of bolt won't cause any issues left where they are.
If you're absolutely set on refitting this kickstand, then those two nubs have to come out. Here's how I'd approach it.
Organise another bike to ride while you're working on this one. It might take days, and having another ride means this one can be worked on and left to soak.
Remove the wheels for access, find space to work where you can leave the bike overnight.
Clean the dirt off with water, dry, and then soak down the area with penetrating oil. WD40 is not penetrating oil
Does the bolt poke out from the frame at all? You might be able to get pliers on it and rotate gently. Another option is to use a "dremel" and a thin cutoff wheel, or a hacksaw to place a slot in the end of the bolt for a flathead screwdriver or manual impact driver.
A punch and hammer can help to rotate the bolt on its threads.
You can also apply gentle heat to the area to help the penetrating oil creep better. I use a workshop hot air gun, though a hairdryer can work too. Do not use any kind of open flame because it will damage the paint.
Patience and Gravity are tools too - soak it in oil again and leave to stand overnight.
Graduate to making holes. If you have access to left-hand drill bits, they can be useful here because they will push against the stuck threads. Be very careful to be centered (a punch mark to start can help). Start with a 3 or 4mm hole, so it doesn't risk touching the threads of the frame.
A pro machine shop would make a flat spot with an endmill or a center drill or spotting drill and then go in.
At this time you might try your "easy out" but in my experience they're not likely to help. Do NOT hammer them in. Use a tap handle to turn them so you get feedback. If the easy out snaps off, it will be even harder to fix this.
Next is to drill out the entire core of the bolt stub but only just grazing the frame's material. This should leave a spiral of metal from the bolt in the frame which you pull out like a string. This drilling op must be straight and centered. Then "chase" the threads with the correct tap.
So you've drilled into your frame and the thread is damaged. Your only option here is a helicoil thread repair. That's certainly possible in the home shop, and I've done it but too complex for this answer.
Finally when you have both stubs out, use top quality high-tensile bolts. Avoid random bolts from the gack box, get yourself some grade 8 bolts of the right thread and length. This will stop the bolts from snapping again.
When you do reassemble, use copper clay or a good grease between the bolts and the frame. That will limit corrosion in the future.
Good luck !