Is a delivery app allowed to send my Google customers to its homepage?

Not under Google's rules. A provider link must go straight to the orderable menu, never to the provider's homepage.

• The customer must be able to finish without a phone call or another site.
• The first step must not require sign-in.
• Payment details must not be asked for until items are in the cart.
• You can remove a provider link under Food ordering, then Remove link.
• Providers must remove the link within 5 business days of your request.