Tabbed: AI chatbot in New Tab/Sidebar wót DerivedFunction

A new tab page with an AI-like user interface. This extension does not, and will not send data to any other third parties other than directly to AI chatbots (ChatGPT, etc) you want to interact with.

Features
Note: You may have to sign in for each AI chatbot for it to work..

Basic
- Clean UI adapted from ChatGPT and Grok
- Ability to switch between different AI chatbots/websites
- Paste text into the prompt
- Search Everywhere runs parallel queries across multiple AI chatbots
- Eight default suggestion ideas to save time on commands.
- Omnibox commands (type "tb @cg Hello" in the address bar")
- Click on the extension icon to directly open your current AI chatbot.
- Permissions are optional but extend the basic features. You can revoke them any time by pressing "reset" in the options menu.
- Context menus provide suggestions as your browse

Optional Features (in Options)
- Allow a custom name for greeting
- Hide or display suggestions
- Set weather and time
- Set light/dark mode
- Set the background Image using Unsplash/Pexels, or your own image.
- Fade the chatbox after inactivity

Experimental Features (In Experimental)
- Gemini, DeepSeek, and Qwen support via content scripts.
- Paste Images onto the prompt
- Advanced search with Web Search, Deep Reasoning, and Canvas.
- Other AI chatbots with the "beaker" button also allows support for content scripts, but is not required
- Send queries to the same chat