collab: Use StripeClient when creating Stripe Checkout sessions (#31644)

This PR updates the `StripeBilling::checkout_with_zed_pro` and
`StripeBilling::checkout_with_zed_pro_trial` methods to use the
`StripeClient` trait instead of using `stripe::Client` directly.

Release Notes:

- N/A

crates/collab/src/api/billing.rs

@@ -338,13 +338,11 @@ async fn create_billing_subscription(
     }
 
     let customer_id = if let Some(existing_customer) = &existing_billing_customer {
-        CustomerId::from_str(&existing_customer.stripe_customer_id)
-            .context("failed to parse customer ID")?
+        StripeCustomerId(existing_customer.stripe_customer_id.clone().into())
     } else {
         stripe_billing
             .find_or_create_customer_by_email(user.email_address.as_deref())
             .await?
-            .try_into()?
     };
 
     let success_url = format!(
@@ -355,7 +353,7 @@ async fn create_billing_subscription(
     let checkout_session_url = match body.product {
         ProductCode::ZedPro => {
             stripe_billing
-                .checkout_with_zed_pro(customer_id, &user.github_login, &success_url)
+                .checkout_with_zed_pro(&customer_id, &user.github_login, &success_url)
                 .await?
         }
         ProductCode::ZedProTrial => {
@@ -372,7 +370,7 @@ async fn create_billing_subscription(
 
             stripe_billing
                 .checkout_with_zed_pro_trial(
-                    customer_id,
+                    &customer_id,
                     &user.github_login,
                     feature_flags,
                     &success_url,