Evaluate conditionally intializing REST APIs

[kalessil]

Description

We have at least two places where the rest initialization happens (add_action( 'rest_api_init', ... );).
To avoid unnecessary runtime operations, the initialization can be conditional - can be a wrapping if-statement around adding the hook or inside the invoked methods.

Note: the conditional ideas are

• relying to WC()->is_rest_api_request()
• match the rest URL to include @^/wc/v3/payments/.+@, that'll guard our rest APIs from loading in the wrong context.
• relying to get_current_screen()
• relying to doing_action( 'woocommerce_admin_shared_settings' )

Acceptance criteria

• We evaluate that there is no higher-level logic which does it already
• CI checks pass after any implemented changes

Additional context

• The side-quest discovery of p1715098461138369-slack-CGGCLBN58
• Ideally, we don't need such checks, but from the linked context, we have this code fragment and want to explore if we can skip this context for loading our rest