The Chrome devtools work by connecting to the browser using the Chrome DevTools Protocol. You can find a description of it here: https://chromedevtools.github.io/devtools-protocol/
Another tool you might have heard of that uses the Chrome Devtools Protocol are NodeJS APIs for remote-controlling browsers: Puppeteer (from Google), and Playwright (from Microsoft). You can access the underlying CDP connection from Playwright: https://playwright.dev/docs/api/class-cdpsession
Chrome extensions can add tabs to the Chrome devtools built into the browser. So, a competitor dev tool can be distributed as a Chrome extension and opened with the devtools keyboard shortcut. A user can “switch” to the alternative devtools by put the tabs it adds first and hiding the built in devtools tabs.