[pickers] Support changing start of week day on AdapterLuxon

[LukasTy]

Created from: #10790 (comment)

Do I understand it correctly that after the recent change, we no longer support changing the start of the weekday on Luxon adapter by overriding the getWeekdays method?

Yes, it's an unexpected regression that we must adress somehow I guess. I would like us to discuss if we have a better solution than this override. Two APIs that I can think about:

• a prop on LocalizationProvider to set the start of the date that would only be used by Luxon, just like moment uses the dateLibInstance prop
• a new static method on AdapterLuxon (AdapterLuxon.setCustomWeekStart) that returns a Luxon adapter with the correct start of week

There is also the concern of whether we are willing to risk breaking something we don't know.
Luxon currently doesn't support such a feature natively, because the Intl API doesn't have the full support of getWeekInfo: moment/luxon#954

Considering our position as "consumers" of the given library, we could simply refrain from coming up with custom implementations until a native one is provided by luxon. 🤔

Relevant issue and a proposed custom adapter: #7670 (comment) that we basically broke with: #10345.

Search keywords:

[flaviendelangle]

There is also the concern of whether we are willing to risk breaking something we don't know.

We could provide the method as unstable AdapterLuxon.unstable_setCustomWeekStart.
It would still be more reliable than an adapter method override, but at the same time we could clearly state that we are in an unknown territory.

[carvalheiro]

Hey guys! Do we have any sense of when would this be fixed? I'd be open to work on the change if necessary too 🚀

[flaviendelangle]

Hi,

Do you need any of the features released since this problem has been introduced ?
We started the alpha for the next major and this new method would probably go into it 👍

[carvalheiro]

No, right now we've been using a version that allows the workaround, so we can wait a bit for this implementation. But we will be upgrading it as soon as it released 🚀

[flaviendelangle]

The clean fix will be merged in the v7 alpha branch.
I don't know yet if we will cherry-pick it on v6.

Bu you can apply the exact same behavior [like on this codesandbox](https://codesandbox.io/s/date-
If you encounter any issue, please let me know so that I can fix our implementation.and-time-pickers-forked-ffkc87?file=/src/App.tsx).
You just need Luxon 3.4.4 or above 👍

If you encounter any issue, please let me know so that I can fix our implementation.

[hokwanhung]

In case anyone needs the above URL provided by flaviendelangle (broken via GitHub Issues), below is the target sandbox: