After several days of experimentation, we managed to find a strange but working scheme. I created a website on PHP hosting and made a script on it to call an external API, that is, something like a proxy. That is, I first call the Server Action, from it a PHP script in which an external service is called, I receive a link to the generated PDF from there, and in the Server Action I download the file and send it to S3 storage. Oddly enough, this scheme works, unlike the direct one inside the Server Action.
@George I also noticed while I was looking for reasons that wappler does not update node modules on the hosting and sometimes there is simply no module for the corresponding project functions, especially for modules that are used in third-party extensions - maybe it’s worth making an option to load them when publishing?