Bookings: Support new bookable product type

[itsmeichigo]

Closes WOOMOB-1735

Description

This PR updates the raw type used for bookable products from booking to bookable-service.

Test Steps

1. Log in to a CIAB store with bookings.
2. Navigate to the Products tab > Filter > Product type > Service > Show Products.
3. Confirm that bookable products are displayed in the results.
4. Tap on a bookable product from the product list and confirm that details are loaded on a web view.
5. Navigate to the Bookings tab > All > Filter > Service / event.
6. Confirm that bookable products are displayed in the filter.
7. Try entering any keyword in the search field and confirm that matching products are displayed.
8. Select any option in the filter and select Show bookings.
9. Confirm that matching bookings are displayed correctly.

Screenshots

Simulator.Screen.Recording.-.iPhone.17.-.2025-11-18.at.15.35.57.mov

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• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

[wpmobilebot]

📲 You can test the changes from this Pull Request in WooCommerce iOS Prototype by scanning the QR code below to install the corresponding build.

	App Name	WooCommerce iOS Prototype
	Build Number	pr16362-f68c411
	Version	23.7
	Bundle ID	com.automattic.alpha.woocommerce
	Commit	f68c411
	Installation URL	5t6a1lhpkusro

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.

[RafaelKayumov]

LGTM. All works as expected.