collab: Fully move StripeBilling over to using StripeClient (#31722)

This PR moves over the last method on `StripeBilling` to use the
`StripeClient` trait, allowing us to fully mock out Stripe behaviors for
`StripeBilling` in tests.

Release Notes:

- N/A

crates/collab/src/api/billing.rs

@@ -1182,10 +1182,8 @@ async fn sync_subscription(
                 .has_active_billing_subscription(billing_customer.user_id)
                 .await?;
             if !already_has_active_billing_subscription {
-                let stripe_customer_id = billing_customer
-                    .stripe_customer_id
-                    .parse::<stripe::CustomerId>()
-                    .context("failed to parse Stripe customer ID from database")?;
+                let stripe_customer_id =
+                    StripeCustomerId(billing_customer.stripe_customer_id.clone().into());
 
                 stripe_billing
                     .subscribe_to_zed_free(stripe_customer_id)