Implement V2 gateway label icons on V1 classic checkout

[mdmoore]

Description

Stripe has now added a feature to remove the card icon animations on the payment element (see p1732125470634879-slack-C043JN7AJHY). We would now like to continue with replacing the generic card icon added to the payment gateway label in #9483 with the V2 card icons component.

#10005 handles the checkout block implementation. This issue tracks the classic checkout implementation, which will require a different implementation than the checkout block.

We would like to add these icons to both shortcode checkout.

Note that while this Stripe feature is currently gated to our dev account, we will need to plan how this will be rolled out to all stores. Consequently, while we can complete this integration, we may want to delay on merging and closing this issue, until this rollout plan has been confirmed and aligned.

Acceptance criteria

• Ensure payment element icons animation is no longer present at checkout.
  • May need to test on gated dev account temporarily, see p1732125470634879-slack-C043JN7AJHY.
• Implement V2 card icon label badge with tooltip on payment gateway label.
  • This will need to be present on both shortcode and blocks checkouts, though we may decide to divide this into separate issues/PRs.

Dev notes

Additional context

#9826, #10005