Browser extensions are add-in computer code for a web-browser. Your iPad operating system is designed to be secure - and will only to allow installable computer code (i.e., Apps) to be installed from a trusted source. The iPad system and security architecture is completely different from that of full desktop computers with which you may be familiar.
Desktop computers, such as you PC, permit you to install Applications and “extensions” (consider these to be miniature Applications). In simple terms, all the installed Applications share the memory-space of the computer - and can access each-others data.
iOS/iPadOS is fundamentally different; by design, the iOS/iPadOS system and security architecture uses “sand-boxing”.
Unlike desktop computers, where Applications can access each-others data and system memory, iOS/iPadOS intentionally installs each App in its own private “secure” area of memory. Other Apps cannot access the sandbox of another App.
With this new knowledge in mind, lets think about this concept and its implications for a moment...
Your browser App, from “Developer A”, is installed in its private sandbox. You now install another App (perhaps a browser extension) from “Developer X”; this extension (App) can only access its own sandbox (X) - and cannot access the browser or its related sandbox (A).
This description is highly simplified - but hopefully clearly illustrates “why” the concept of adding an “extension” makes no logical sense with the system architecture employed by your iPad.
The only source of trusted/vetted Apps is the Apple App Store. Either a function is included within the App, or it isn’t. Additional functionality cannot be added to an App, by the App of another Developer.
I hope this explanation is helpful in understanding the [deliberate] limitations of your iPad.