No support for Chrome extensions. Not even support for Safari Web Extensions bundled with iOS apps.
Some browsers do have their own extensions (Edge has AdBlock Plus built-in, but that's all; iCab has quite a few Javascript-based extensions) and of course you get things like using another vendor's bookmark and password sync. But that's about it.
Not really separate. Many extensions designed for other browsers will still depend on quirks of the respective extension implementations, JavaScript engines, rendering engines, etc.
Of course, there are (supposed-to-be-but-aren't) browser-agnostic WebExtensions — but again, only Safari implements them on iOS (starting with iOS 15), they must be bundled with an iOS app, and non-Safari browsers don't have access to those bundled extensions.
Perhaps those browsers will implement support for WebExtensions by some other mechanism but it certainly won't be the case that Firefox for iOS could run extensions intended for Firefox on desktop, nor would one expect extensions from the Chrome Web Store to work properly on Chrome for iOS.
Perhaps that's an upshot? Better support for browser-agnostic WebExtensions?
Even then, that's up to whether or not Apple permits that in the App Store.
Some browsers do have their own extensions (Edge has AdBlock Plus built-in, but that's all; iCab has quite a few Javascript-based extensions) and of course you get things like using another vendor's bookmark and password sync. But that's about it.