Make NewDatePicker reusable

[luacmartins]

Problem

Coming from comment 1 and comment 2 and this thread, the NewDatePicker component is quite brittle since we need to the the route for each new usage. That doesn't scale well and leads to a confusing experience.

Why is this important

We need a reusable "plug and play" date picker component since it'll be used in a lot of flows in App, e.g. bank accounts, requests, etc

Solution

Discuss and find a solution that accounts for the unique challenges of push to page.

cc @Beamanator @mountiny @ArekChr @TMisiukiewicz @burczu @gedu

[melvin-bot]

Triggered auto assignment to @mallenexpensify (Bug), see https://stackoverflow.com/c/expensify/questions/14418 for more details.

[melvin-bot]

Bug0 Triage Checklist (Main S/O)

• This "bug" occurs on a supported platform (ensure Platforms in OP are ✅)
• This bug is not a duplicate report (check E/App issues and #expensify-bugs)
  • If it is, comment with a link to the original report, close the issue and add any novel details to the original issue instead
• This bug is reproducible using the reproduction steps in the OP. S/O
  • If the reproduction steps are clear and you're unable to reproduce the bug, check with the reporter and QA first, then close the issue.
  • If the reproduction steps aren't clear and you determine the correct steps, please update the OP.
• This issue is filled out as thoroughly and clearly as possible
  • Pay special attention to the title, results, platforms where the bug occurs, and if the bug happens on staging/production.
• I have reviewed and subscribed to the linked Slack conversation to ensure Slack/Github stay in sync

[mountiny]

Closing this one in favour of previously created #20630, Bartek from Callstack will work on it once we finish the accountID migration