CustomGPT Deployment via HTML Embed / Embedding GPT in website

Hey there!
I am trying to build a customgpt that i can then host somewhere and embed on my website using HTML.

customgpt.ai is too expensive for me tbh and I want to build it myself using the asisstants API - however i have some questions.

When I write the code, where to I host the code? DO I need to work with AWS? How can I create an HTML embed for my website that my 500+ users can query on my website.

Thanks a lot!