No, it isn't. If you are talking about advisability, the ONLY correct construction is had better, usually contracted to 'd better.

Therein lies the problem.  In comparative constructions, the contraction 'd represents 'would', so many people - including some native speakers - wrongly assume that the 'd' in  "You'd better go" is also a short form of 'would'.  This is wrong. It is never correct to advise someone to leave by saying "You would better go".

So why have you found a page full of 'would better' on Reverso?  The answer's very simple. Look carefully at the sentences. In each case ( apart from number 2, which is incorrect), you're dealing with a straightforward second conditional.  For example, 'either approach would align' or 'such policies would respond'.  The 'would' here is not connected to the adverb 'better' : it's connected to the verb, and it could be replaced with any suitable modal e.g. 'such polices might better respond' or 'such policies will better respond'.  These sentences are formal, but they have nothing at all to do with the fixed phrase 'had better' meaning that a course of action is advisable.

I hope that makes sense.

Su Ki is correct.

Jimena,

In your examples, you have made a few mistakes: 

 "It would better that italki users give more context...= WRONG

This should be    It would be better if...

As SHL says above, you could say It would better the italki community if..., but that is a different construction.

It had better that Italki users give more context...= WRONG

This should be    It would be better if italki...

You had better listen to Julie or... =This is CORRECT, but we would contract it to You'd better.   Because this sounds very similar to "You better...," some people say this.  This is not correct, however. (Unless you are a linguistics major, and then every God-forsaken thing out of the lips of mortal man is "correct" as long as you are a native English speaker. :)  )  It is the same as the situation where native speakers say" I would of gone" because they do not understand that it is I would have gone which contracts to I would've gone.  They are confused by the sound.

You'd better not  shout.

You'd better not cry.

You'd better not pout.

I'm telling you why.

Santa Claus is coming to town.

you can use "would better" when it is considered that something would serve, or do, or provide something that gives an advantage. 

This is what all the examples of "had better" are doing in your link. (for specific situations ).

"it would better that itlaki users give more context to many of their questions." <-- (does not apply to your question)

I would be better if italki users could give more context to many of their questions" <-- a better more natural daily speaking way of saying the same thing.

"had better" = suggesting or telling someone that something needs to be done or something will happen. In the present or future. 

https://dictionary.cambridge.org/grammar/british-grammar/modals-and-modality/had-better

uuhhh  I think I must disagree.  "would better"  I only use in one specific situation.  For your question my little American brain is telling me that just "better" for advice is by far the correct choice.  "Had better" is used but only sometimes. "Had" to me seems like a useless word in this situation. Here are some examples :  

 " You better  listen to Julie or you will get hit by a car"  

 " You had better listen to Julie or you will get hit by a car"      #1 sounds way more natural and I don't think I would ever use #2.    Both examples "better" means "need to" or "should" else something bad will happen. 

Anyway that is my opinion. 

" Would better" is only used in this type of situation.   " Juan would better fit in another class because of his behavior."   

But I would rarely use this phrase because there are easier ways to say it.