I had a idea for a Chrome-Extension that would translate the contents of a Webpage 100 times (variable by a slider) and finally translate it back to the original Language for some funny outcomes (like with the Bad Translator google docs addon but instead of having to manually paste text there i could just translate the whole webpage and make it look funny) but the problem is, that I would need a expensive api key. I, however, noticed that when you google google translate, then you can translate for free, so my idea would be to just feed the websites text into that thing the ammount of times that were specified. How would i do that automatically?
You can try to use the Network tab in your browser's developer tools (F12) to intercept the relevant HTTP request so you can craft your own similar HTTP requests. However, this is likely to be unreliable because of temporary tokens in request headers and because of CAPTCHAs. You could try instead using something like selenium to automatically open a browser and interact with Google that way, but you may still run into CAPTCHAs and would not be able to do this within the browser extension, and it might not be practical to offer a free hosted service doing this. It is also likely that Google would reject your extension due to unauthorized use of their internal APIs.

Ultimately, machine translation uses a lot of computational resources, and companies operate at a loss when offering it for free, so they will do their best to lock the free version down as much as possible to prevent abuse. Instead of attempting to find ways around abuse prevention, consider legitimate alternatives such as embedding a tiny m2m translation model inside the browser, other APIs such as TextSynth or DeepL, or find less complicated ways to mess with the contents of a webpage.