How to programmatically solve Rotate Captcha using the API of the 2Captcha service - a description of the method, the order of actions, examples of scripts - https://2captcha.com/p/rotatecaptcha
Demo page with examples of captcha https://2captcha.com/demo
Sources on GitHub at the link https://github.com/2captcha/2captcha-php
Here are examples of decision method scripts, configuration descriptions and an error handler.
Registration in the service https://2captcha.com/auth/register