Hello Hippolyte,
Do you want to create a new payment page in Odoo or integrate with a new payment provider whose credit card form should be present on existing payment pages?
In the first case, you can take inspiration from https://github.com/odoo/odoo/blob/16.0/addons/payment/controllers/portal.py#L36C1-L151, which controls the page for payment through payment links. It calls only the essential methods for preparing the payment page. You can also have a look at https://github.com/odoo/odoo/blob/16.0/addons/account_payment/controllers/portal.py#L13-L68, which does the same job but for the portal page of invoices.
In the second case, it depends on the provider you want to integrate with and the features you plan on supporting. The payment
module serves as a framework for integrating payment providers in its own module, and you should only need to override some methods and create one or two views to have everything working. I recommend taking examples from existing payment_*
modules.