How can I repair this water damage area in my "laminate"(?) countertop near my sink?

Question

I'm renting and don't want to have to pay my landlord for an expensive countertop replacement, so I'd like to know how this can be fixed. Also, there is some potential replacement material hidden beside the stove and fridge. [EDIT: When I first posted this, I called it "laminate". Then considered maybe "Contact paper" aka "Peel and stick" countertop. I think the final determination is this is possibly just paint, see end of post.]

Here's the damaged areas, under the switch and the outlet. (Note, dishwasher is seen at bottom of image. Might be a factor.)

Close up of switch damage.

You can see that the laminate/plastic has bubbled away from the substrate. This runs to the left and right of the cracks.

The outlet damage is similar. Water might have got in both places from the top, as it is exposed over both switch and outlet.

Theory #2, as indicated in an answer below, this might be considered a design flaw (not our fault!), and the thin material might be getting warped due to steam/humidity. A good theory, since the dishwasher is just below it. You can see the upper-right corner of the dishwasher at the bottom of this first image.

EDIT: I think it's just paint? The same pattern is on the outlet

Chipping on the front edge:

View from under a corner:

Final Update: So the maintenance man comes in, says no that's not water damage, it's just really cheap spray on, they all do that. Then pulled out his silicone caulk, laid down a bead, and wiped it with his finger.

Answer 1

It's a design flaw, not actually your fault.
[Final damning analysis at the end.]

I've seen two types of that 'not-really-laminate', it's either a heat-bonded plastic or a really, really thin layer of actual mica. Neither is at all tolerant of water penetration. In that respect they're both like 'proper' mica laminate, but worse because they will both bubble badly.

If you have the plastic type, you can - if you get the sockets out of the way first - gently heat it & smooth it back into shape. You'd then have to glue & clamp it to try persuade it to stay that way. Then you can silicone it all to seal it.
If it's actually mica you'll never persuade it back into shape, it will just fracture, leaving you sticking bits of mica jigsaw back into place one at a time.

So no, it's never going to fit back perfectly - partly because it will not re-shape accurately & partly because the wood underneath is shot too. It may pass casual inspection.
As a friend of mine would say, "A blind man on a galloping horse would never notice it."

Alternatively, blame it on whoever put mains sockets through it in the first place. I would call that 'not to code' for distance to sink & height above worktop*, though that may depend on where you live.
I'd have put them above that splashback, not through it.
For them not to have sealed around the sockets was the second failure. I can imagine the fail would have started by water/condensation/steam penetrating from above the sockets, eventually causing damp below them.

Alternative two… find a new piece of matching splashback & this time seal it in properly in the first place. You said you have some potential spares - they'd be your cheapest option.

A late thought - whoever tightened in that socket pulled it back not only hard enough to bend the patress, but also bend the splashback, either before or after it was weakened by the water ingress. That could have caused a fail in the silicone before the visible trouble started, as the wood was slowly being pulled away from the sealant line.
That's going to make clamping it much more difficult, as your flat clamp isn't going to sit flush, & your new silicone seal is going to have a 'flood plain' in the middle. It makes replacement by far the best option now.
*and also on closer inspection because they left a gap at the top you could poke something into

After more comments, it was discovered this is actually a spray-paint speckle finish, right over the plugs. No tenant should accept any responsibility whatsoever for this type of bodge job not performing to expectation.