Goal
Get access to https://calendar.google.com/ (Google Calendar) in a Google Web App HTML page that can be altered with HTML/CSS/JavaScript.
Questions
How do you place a google service directly into a GAS web app? Are there any indirect methods to achieve this?
Background:
I have been developing full stack Google web apps for businesses for a few years and repeatedly have clients asking to have Google Calendars or other google services integrated into these tools. When it comes to the maps service there is currently full functionality. However when it comes to calendar, there only seems to be an option to embed a limited and simplified version. It lacks the capability to be edited directly within the webpage, the style overrides any CSS attempts I have made, and the ability to even set the color of the events within a displayed calendar are unavailable. I've tried to open https://calendar.google.com/ directly into an iframe through Google Apps Script (GAS) and altering restrictions but all attempts made return an error.
Other questions I have seen on this topic only ever discuss embedding that dumbed-down calendar. That is not what I am after.
I also cannot use most third party resources due to the sensitive nature of the company data that will be in use.
Thank you for your time.