Building embeddable widgets

I'm looking into building a product that will be embedded and loaded externally on customer websites.

Think of the Intercom chat widget, for example, it's loaded externally.

I wonder about technology to use and the process how to build injectable script that will embed my widget. Is there any ready to use solution or I have to write everything from scratch? Can I use a framework? Do you have any experience in that topic or articles to share?