The only rule in a simple sentence that usually holds is "Finite verb at second place".
For the OP’s simple example we have another rule: In the middle field the unstressed pronoun
es have to take the first position. Neither the adverbial nor the object can take this position, when
es is in the middle field.
In diesem Wald gibt es viele verschiedene Bäume.
* In diesem Wald gibt viele verschiedene Bäume es.
Viele verschiedene Bäume gibt es in diesem Wald.
* Viele verschiedene Bäume gibt in diesem Wald es.
This rule is very strong and by the way: you cannot emphasize this pronoun in the example, can you?
The only rule in a simple sentence that usually holds is "Finite verb at second place".
In general, this rule is not so strong.

We don’t even need any contrast to break this rule. Often we find an adverbial and the subject or an object before the finite verb (cited from DeRoKo):
Vermutlich ein indigener Künstler hat den Codex zwischen 1570 und 1595 gezeichnet, mit den damals üblichen natürlichen Pigmenten und Farben.
Süddeutsche Zeitung, 29.11.2017
Wenigstens den Briten würden solche dreisten Betrugsversuche ohnehin nicht einfallen.
Süddeutsche Zeitung, 06.07.2019
These examples are not rare!
Durch den Wald fliegt ein Vogel leise. (Er fliegt durch den Wald nicht laut. But the base meaning is here: Im Wald ist es still. Der Vogel stört die Stille nicht.)
If leise is in contrast to laut, it may beat the end.
Ein Vogel fliegt durch den Wald leise. Laut aber kreischen die Sägen im Sägewerk. (Base meaning is contrast.)
Sorry, I wouldn’t accept breaking the rule given in
#5 here.
It is weird, and it depends on context, but grammatically it is correct, if both syntax and semantics are correct. If you try to use the phrase with wrong meaning, the syntax will be blocked.
I give a second example:
Ein Vogel fliegt durch den Wald leise, aber hundert Vögel machen ziemlichen Lärm.
One bird flies through the forest silently but hundert birds are quite loud. (This is kind of interlinear translation.)
I wouldn’t …
Edit: Chomsky once wrote:
Farblose grüne Ideen schlafen wütend.
This seemed to be a correct nonsense sentence. Later it became a sentence with sense.
Of course, this sentence is correct: subject · finite verb · predicative or adverbial. I can’t see any broken rule here.
The sign "*" means: grammatically wrong - as far as I know - it does not mean "strange".
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I do not understand what is wrong with my sentence.
It breaks the rule given in
#5. Please, can you give an authentic example for what you state? I do understand what you state and I admit that contrast can change the order of adverbials in general, but I don’t believe that authors would change the order of adverbials of manner and of direction – before any comma or dash. There are other possibilities to express contrast: »Der eine … die anderen …« or »Ein … die anderen aber/jedoch …« Of course, other possibilities don’t make your sentence wrong, but I can’t accept your constructed sentences. Please, give an authentic and serious example.