While the other answers are correct, and they probably allow you to plow ahead with whatever you had going on, I think the actual intent of your question should be addressed.
In general, you seem to be concerned that one effect says "cannot be countered," and another effect that says "counters anything."
It is essentially like the conversation you hear sometimes among comic fans which goes something like this...
What happens when an unstoppable object meets an immovable force? Such
as superman and hulk.
That is essentially the idea that you seemed to be trying to get at. Putting your question this way...
What happens when an uncounterable effect meets an effect that can
counter all other effects?
If the 9th level spell "Super Mega Ultra Counter" says "Can counter anything and everything without exception."...
...and the 9th level spell "Uncounterable Fire" says "Rains fire destruction down and cannot be countered by anything at all whatsoever"
... then you have run into this problem. So PC 1 uses Uncounterable Fire and PC 2 uses Super Mega Ultra Counter, but either PC saying theirs takes precedence would be correct, and they would both be wrong.
The only way that the rules could account for this is if the description for Uncounterable Fire said "... by anything at all whatsoever except Super Mega Ultra Counter", in which case the counter would fail, or if Super Mega Ultra Counter explicitly said "... by anything at all whatsoever except Uncounterable Fire." Either of these two changes would obviously make the rules work, but without one or the other then the rules are broken... except for the fact that when the rules are not sufficient we have the DM-backup rule.
In that case, all other things being equal, it is completely up to the DM. By default, it has to be, even by a "literal interpretation of the rules" as you asked for.
Since you might be asking from the DM's point of view and need some ideas...
You could rule that the universe is not equipped to handle this undefined interaction and any random thing happens. If taken this route, a simple reaction would be an explosion or a black hole. But since the outcome is undefined and literally the very universe itself might not be equipped to handle a situation of this nature, where its own rules conflict with themselves, "any random thing happens" is meant very literally.
The universe could crash. This could take the form of the universe unravelling and destroying itself (probably not a good DM choice for something as simple as a wish in a certain area, otherwise the deities may have destroyed the universe long ago), or a universe crash could result in a "groundhog day" style loop where the universe tries to replay the previous day to try to get a different outcome (players keep replaying that day until the PC does not cast wish there), or if the universe has good error handling it could simply mean nothing happens.
Other random things that could happen if the very universe itself does not know what to do: everything in sight turns pink, or turns into sheep, or gravity starts changing, or pick spells at random and they start spontaneously occurring in the area with random targets for some amount of time.
Or, as user2015 points out, you could just decide that one of the effects is stronger than the other. For example, in the case of superman vs hulk, you could just decide that one of them is stronger than the other. In your specific case, it seems reasonable to suggest that the deep healing power of the plain is stronger than a PC caster. Or, if you want to think of wish as being all powerful, you could claim that wish is stronger than the power of the plane.
Personally, if I were DM'ing a situation like that I would just say that the plane's power is strong enough to do exactly what it says, and I would even say the wish's negative effects are all healed. Even if the wish was stressed and the caster hit the "no more wishes for you ever" barrier, I would let the plane undo even that, making it an optimal place to use wish. For this very reason, creatures which can cast wish might venture from far away just to cast it in this wish-safe zone. It could even make for good adventures for the PCs if they are aware of it.