PRB/ECE refactor to utilize tokenized carts

[frosso]

Created as part of #8298 , following the investigation outlined on pbIwZe-1Mr-p2

1. Integrate the new API on PDPs
   • To ensure seamless functionality and compatibility
2. Integrate the new API on block-based cart & checkout pages
   • To make the integration “easier”, since they are both using the Store API
3. Integrate the new API on shortcode cart & checkout pages
4. Cleanup of the old implementation
   • This includes JS-related code, but also (now) unused custom endpoints

The multi-step approach could be executed in two ways:

• Implementing the new functionality on the existing JS files (like I did in my POC)
  • This approach involves integrating the new functionality directly into the current JavaScript files, aligning with the existing code structure
• Implementing the new functionality on new JS files
  • Creating separate JavaScript files dedicated to the new functionality

Although the second approach may initially introduce a slight uptick in complexity, I believe it offers distinct advantages.
It can pave the way for a smoother cleanup phase, enabling clearer isolation between the old and new implementations. This separation enhances code clarity and lays the groundwork for envisioning a future where solutions between WC Stripe and WooPayments can be seamlessly shared.

External dependencies

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1. woocommerce_rest_invalid_address_country on guest checkout order w/ no shipping needed woocommerce/woocommerce#53032
   focus: store api priority: normal team: Rubik type: bug +4
2. [Enhancement]: Discrepancy in Email Requirement Between Classic and Store API Checkout Flows woocommerce/woocommerce#48540
   focus: checkout focus: store api needs: discussion priority: normal team: Rubik type: enhancement +6

Third-party extensions

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1. https://github.com/woocommerce/woocommerce-deposits/issues/665
2. https://github.com/woocommerce/woocommerce-composite-products/issues/1207
3. https://github.com/woocommerce/woocommerce-product-bundles/issues/1483
4. https://github.com/woocommerce/woocommerce-product-addons/issues/1154

Issues that will be fixed once launched

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1. Compatibility: Advanced Shipping Packages – shipping cost not updated in payment request modal #5657
   category: core focus: checkout payments priority: medium status: blocked type: bug +5
2. WooPayments Sends Wrong Total (Decimal Places) to Google/Apple Pay When Using Hungarian Forint #8277
   Component: International Expansion focus: checkout payments priority: medium status: blocked type: bug +5
3. Order origin with ApplePay/GooglePay #8784
   focus: payments acceptance & processing priority: low type: enhancement +3
4. Payment request buttons Incompatible with WooCommerce Product Bundles #3147
   category: projects focus: checkout payments priority: high status: blocked type: bug +5

[frosso]

Since it's not linked here, the completeness of this project is also dependent on woocommerce/woocommerce#48540

EDIT: related to the above - I noticed another difference compared to the old flow: pay-for-order orders without a shipping address fail to process when using the Store API.
https://github.com/woocommerce/woocommerce/blob/trunk/plugins/woocommerce/src/StoreApi/docs/checkout-order.md#process-order-and-payment

EDIT 2: turns out that the shipping address discrepancy has more steps related to it - it also requires physical products on the main customer's cart.