A browser extension can technically read anything on the page if it is granted that permission. Docognito requests only storage permission and does not log keystrokes: it relays what you type into the real composer and keeps no record of it. Check any extension's permissions in Chrome before trusting it near a page full of typing.
What a permission actually grants
Every Chrome extension declares, in a file called its manifest, exactly what it is allowed to touch. Some permissions are narrow, such as storage, which lets an extension remember a small amount of settings between sessions and nothing more. Others are broad, such as being granted access to read and change data on every website you visit, which is close to the maximum access an extension can hold.
Chrome shows you the relevant part of that list before you click install, so the warning you see at install time is not marketing copy written by the developer. It is generated from the manifest itself, which is why comparing two extensions' install warnings tells you something real about how they differ.
The permission that decides page access
The permission that matters most for a question like "can it see what I type" is not storage, and it is not any single named capability. It is whichever entry in the manifest gives the extension a content script on the page you are looking at. An extension with that kind of access can, in principle, read the page's text, watch its keystrokes and change anything rendered on it, because that is what running code on a page means.
That is also true of extensions that behave well. The distinction between an extension that could log your typing and one that actually does is not visible from the permission alone. It comes down to what the code does with the access it was given, which is not something a permissions screen can show you directly.
What Docognito's manifest actually requests
Docognito's own manifest requests one browser permission, storage. That entry controls a small settings object: whether the disguise is on, whether dark mode is chosen, and the document title you typed into the fake title bar. None of that is your conversation.
Its content scripts run on claude.ai, chatgpt.com and chat.openai.com, and no other website, declared by name in the same manifest and shown in the same install prompt, rather than on every site you visit. That scoping is why the extension can redraw the visible page, redrawn as a document editor and rewrite the browser tab title and the tab icon on those three sites specifically, and cannot touch anything running on any other tab.
Why touching your typing is not the same as logging it
Here is the part worth being precise about, because glossing over it would be dishonest in the other direction. The disguise does need to see each key you press. It has to, because the page you are looking at is not the real composer, and every character has to be routed from the surface you are typing into across to the one Claude or ChatGPT actually reads, or sending would not work at all.
What it does not do is keep any of that. Nothing about the words you type is written to storage, held in a log, or sent anywhere beyond the one page already reading it. Close the tab and nothing about what you typed persists inside the extension, because there was never anywhere for it to persist to.
This covers Docognito specifically, not every extension in your browser
Docognito requesting only the storage permission is true of this extension and says nothing about any other extension installed in the same browser. A different extension can request, and be granted, far broader access, including the ability to read every page you visit.
How to check any extension for yourself
Open chrome://extensions
Chrome's own extensions page lists everything installed, active or not, with no need to trust a marketing page to find out.
Click Details on the one you want to check
Chrome shows the exact sites it can run on and the exact permissions it holds, generated straight from its manifest rather than written by the developer.
Compare that list against what the extension claims to do
An extension asking for far more than its stated purpose needs is the clearest warning sign available, and it costs nothing but a minute to look.
Checking what an extension actually asked for
An extension can see what you type whenever it is granted access to the page, and no single tool changes that fact about how browsers work. What you can check, in seconds, is exactly what each extension actually asked for. one browser permission, storage, scoped to claude.ai, chatgpt.com and chat.openai.com, and no other website, is what Docognito asked for, and it is worth confirming that for anything else running in the same browser rather than assuming it.