What is Crypto Payment Forwarding and how does it work?

[apirone.com]

A non-custodial acceptance of payments implies that a client provides addresses or xpub of HD wallet (BIP32) for transaction tracking and payment notification. Such services have been blockchain.com, bitcoin.com, and blockonomics.io until recently.

Payment forwarding is an instant transfer from a temporary crypto address to the address of the recipient, with notifications (callbacks) about transactions. Such services are, for example, gourl.io, and opennode.com. Apirone also provides the services of forwarding, and soon we are going to launch a non-custodial wallet. For more details look at our website.

How does forwarding work?

https://miro.medium.com/max/1400/1*wyiWRuN-XzO_qArS-4xcEA.png
A temporary address is generated for each payment.

It is needed to identify the order, since a customer can pay partially, from different sources, or at different times, for example. If you use the same address to receive payments, it is difficult to determine who paid you, when, for what, and how much.

https://miro.medium.com/max/1400/1*0oOXaK1cYe9dVOdH6oJ5Ng.png

Wallets managed by third parties can be insecure and vulnerable since the payment provider can request KYC verification or even block funds themselves. A vivid example is the consequences of sanctions: processing companies that prohibit the use of your own money; exchanges that decided not to return clients’ assets; services that stage a hacker attack and the loss of all client funds.

Forwarding is an intermediate option between custodial and non-custodial processing. This is a great way to start and roll out your new projects quickly.

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A non-custodial acceptance of payments implies that a client provides addresses or xpub of HD wallet (BIP32) for transaction tracking and payment notification.

The txid is all you need to track a transaction on the blockchain and there are lots of services that can be used to achieve this.

The other parts of your thread are a bit confusing to me or not well explained.
For one;

If you use the same address to receive payments, it is difficult to determine who paid you, when, for what, and how much.

It is not actually difficult to determine this. On checking your wallet on electrum, you can easily view each input and the sender's address. You can also do this through a block explorer.

Forwarding is an intermediate option between custodial and non-custodial processing. This is a great way to start and roll out your new projects quickly.

Why would one need an "intermediate option" when they can easily stick with the safer option of a non custodian process?

[decodx]

A temporary address is generated for each payment.

It is needed to identify the order, since a customer can pay partially, from different sources, or at different times, for example. If you use the same address to receive payments, it is difficult to determine who paid you, when, for what, and how much.

So, you are talking about crypto payment gateways and processors? Like BitPay or Coinbase Commerce?
Yes, crypto payment processors are a must for any business that wants to accept cryptocurrency payments. But there is also a self-hosted non-custodial solution - BTCPay Server.

Forwarding is an intermediate option between custodial and non-custodial processing. This is a great way to start and roll out your new projects quickly.

I don't think there's an in-between option between custodial and non-custodial processing. A wallet can be either non-custodial (you hold the private keys) or custodial (the company holding your coins does). There is no middle ground.