WordPress. How to allow payment only after order confirmation?

Question

WordPress

Greetings.

There is an online store on wordpress. I'm trying to find a competent and more or less automated solution to the following problem. The client (buyer) puts the product into the cart, then from the cart to the checkout and pays ... the scheme is normal, but we need the client to be able to pay the invoice only after the order is confirmed (because not all products are in stock).

I had an idea using the plugin to remove the payment form from the checkout, but for the order to be created. Then the manager checks it and changes the status of the order from "in processing" to "waiting for payment". And after changing the status of the order, a letter is automatically sent to the client by mail, in which the invoice and a link to payment. He clicks on the link and gets to the page where the payment form is set.
If it is important what the payment will be - alphabank.

How to make a custom status - I found. I also found how to send a letter when changing status (although I'm not sure if this is the right solution). But I have no idea how to send a payment link in a letter. We are planning only one payment method - the form of Alfabank.

Tell me please - how to send a letter (automatically) when changing the status of an order? and how to insert the correct payment link in this letter (so that the payment is for this particular order)?

Thank you very much)