[pickers] Always use props.value when it changes

[flaviendelangle]

Closes #10424

[flaviendelangle]

We need to store the raw props.value variable if we want to do a reference comparison

[mui-bot]

Deploy preview: https://deploy-preview-15490--material-ui-x.netlify.app/

Generated by 🚫 dangerJS against 8fac8d9

[flaviendelangle]

We compare the old props.value with the new props.value (without any processing done to it)
If it changed:

1. We set the new props.value in the state
2. If the new derived props.value with the right timezone is not equal to the current draft, we update the draft

[github-actions]

Cherry-pick PRs will be created targeting branches: v7.x

[LukasTy]

@flaviendelangle I think that the PR only partially fixes the issue.

Essentially, we should always keep the bound value as the source of truth, even if it didn't change.

In this example, any change should not change the value as with the native input.
https://stackblitz.com/edit/react-ly6xoy?file=Demo.tsx

[flaviendelangle]

I think we can create a dedicated issue for this exact behavior: #15530
It's not only at the picker level, it's mostly the field that works this way. I do agree that it would be nice to mimic to browser input here. The main challenge will probably be to handle invalid date correctly.
We might also have a breaking change if people do checks before storing the value in state and they don't handle invalid values correctly.