I understand the desire to replace everything (even when its working fine). After a considerable bit of experience in life, I leave be things that work. If I were you, I'd leave good bearings in the bike and reassemble. My two cents: ignore as you see fit. I'm an engineer and can get a bit OCD about everything being perfect so I understand the “make everything new” sentiment.
But you've got a project.
First, some terminology. The tube on the top of the fork is a steerer tube. The tube in the frame that the steerer tube goes through is the head tube. The bearings, spacers, etc. that allow the fork to turn in the head tube is the headset. Your goal was to replace the headset bearings.
It would appear that you have a threadless headset, with sealed bearings. See the pic below. So you have a frame (which I think is alloy, from your pic). You have a bearing cup on the top and bottom of the head tube. These hold the bearings. Do not knock these out. You have the bearings in the cups, and (if we are reading the picture correctly) there is a retaining wire that fits in a groove in the cup and holds the bearing in. See the pic.
To get the bearing out, the first step is to remove the retaining wire. A small screwdriver should allow you to pry the end of the wire out of the groove and up. Then hold the wire out and go round the circle to remove the whole wire. Once that’s done you can try to push the bearing out with a screwdriver. Two things. First, make sure that you are pushing out the bearing, and not the cup. The cup stays where it is through all this. The next point bears on knowing that the bearings have inner and outer races. The cup is holding the outer race. In installing or removing (for later use) a bearing, NEVER TRANSMIT SHOCK FORCE THROUGH THE BEARINGS. That is, your screwdriver should push on the outer bearing race to remove the bearing, and you should not try to push the outer race out of the cup by pushing on the inner race. If you used the screwdriver, again, it’s tippy tap on one side and then tippy tap on the other side, making sure that your screwdriver is driving the bearing, and not the cup. If the bearing won't come out, you'll need a headset bearing removal rocket. Park Tools offers one. Look it up.
You need what is called an upper cone to replace the one you umm... artistically modified. This has a cone on the bottom that fits into the chamfered inner edge of the bearing that is shown in your pics. If you can figure out the brand you have, you might be able to order a replacement but I suspect you won't be able to ID the brand. So when you buy your bearings, get a compatible cone.
If you choose to remove the bearings, in addition to the bearing removal rocket, you will need a headset bearing installation tool. Again, look this up. A cheaper alternative is to buy some allthread (say 3/8 inch) and some nuts and washers. Again, make sure that the washers are pushing on the outer race to seat the outer race in the cup.
Check out
to see how headset maintenance is done. And
to figure compatibility.