[ResponseOps][Rules] Use the new rule form to the create rules flyout

[cnasikas]

In #175634 we implemented the new rule form. We should use the new rule form on the create rules flyout.

Related: #179108

Designs: https://www.figma.com/design/zetHXnUP0YnDG4YmvPwRb8/Adapt-new-Rule-form-to-work-in-flyout?node-id=1-191&node-type=canvas&t=PyPLu7smPOf1cqj9-0

DoD

Beta Give feedback

1. Create a package called @kbn/response-ops-rule-form under packages/response-ops and move all the code related to the rule form from the @kbn/alerts-ui-shared. Types or code used in other places should not be moved and can be imported by the @kbn/alerts-ui-shared package.
2. Export the new flyout following the designs where it can be used to create rules using the new rule form.
3. Replace the old flyout with the new one whenever is being used.
4. Remove the old flyout from the triggers_actions_ui plugin along with all related code.

[elasticmachine]

Pinging @elastic/response-ops (Team:ResponseOps)

[Zacqary]

Working on new package task in an initial PR

Lots of code to move and reroute, might be a big job

[cnasikas]

Thanks @Zacqary! No worries. Plz move code relevant to the form. Any types,hooks, etc that are being used either by the @kbn/alerts-ui-shared or triggers_actions_ui or any solution should remain in @kbn/alerts-ui-shared and the new package can import from the @kbn/alerts-ui-shared whatever it needs.