I have the same question. Even the cart icon in my case is not the same as I have in a snippet section, but some default svg…
I see that your post from June 2023. Did you found any solution?
Topic summary
Migrating from Checkout Liquid to Checkout Extensibility removes direct DOM manipulation, preventing prior customizations like hiding the cart breadcrumb/return button or altering header elements via injected JavaScript or apps.
Participants confirm Shopify has locked down checkout DOM access. Requests include hiding the cart link, modifying the gift code field, changing the cart icon, and updating the login/logout URL.
Recent update: Shopify’s Admin GraphQL API introduces branding controls. In the unstable release, CheckoutBrandingCartLink can hide the cart icon (verified via GraphiQL). In the 2024-04 API, CheckoutBrandingHeaderCartLink appears to support customizing the header cart link/icon. Linked docs are central to these options.
Unresolved items: No confirmed method to modify the gift code field or change the login/logout URL/button. Users are seeking a way to edit the login button behavior.
Status: General DOM manipulation is not supported under Checkout Extensibility. Limited customization is possible via the Admin GraphQL branding objects; broader customization requests remain open/ongoing.