CapSoftware/Cap ? reverse-engineered prompt

I want to build an open-source alternative to Loom. It should be a video messaging tool that allows users to record their screen and camera, do quick edits, and then instantly get a shareable link to send to others. The user experience should be beautiful and fast.

The project needs two main components. First, a desktop app for both macOS and Windows that handles the actual screen recording. Second, a web app where users can manage their library of recordings and where the shared videos are hosted for viewing.

A key requirement is that the entire thing must be easy to self-host. Please set it all up to run with Docker Compose, so I can deploy it on my own server with a simple command. For the tech stack, let's use Next.js and React for the web portion, and Rust with Tauri for the high-performance desktop client. The backend should use a MySQL database.