Is there a way to send a message to the chat that contains a script through the API?

I am trying to make an API script that when ready will send a chat entry that contains a script, so it can run on the website itself. If this is possible (or if there is any other way to make a script run on the website through the API) then i can use it to gain access to the document element, which i need for the script, is there no way to do that? and if there is no way, will there be a way in the future?

There is no way for the API to gain access to the DOM in the browser. Neither is there a way for Sheet Workers to gain access to the DOM. Running arbitrary code on users' browsers would be a serious security risk.  If you want things to happen in YOUR browser based on something the API does, you could run a javascript in YOUR browser that monitors the chat and performs some action for a given output. You'd use xJS or Greasemonkey or some other browser extension to do that.