You type, you think, you delete a sentence. Only when you press the button does anything leave. That is how it feels, and it is where most conversations about AI and data start too: at the send button.
True for the model. Not true for the text.
In browser memory
The moment you type a character, it is in browser memory. Unavoidable, and in itself not very interesting.
What sits alongside it is more interesting. Nearly every modern web application persists your input to the browser's local storage as you go, so a half-written message survives a crashed tab or a mis-clicked close button. Nobody objects to that feature, and nobody thinks of it as a data flow either.
The consequence is that your draft outlives the tab. It is on the machine, in that site's storage, until the site clears it. On a shared workstation that is worth knowing.
Sync to the server
Some services go a step further. Drafts are synced to the server so you can pick up on your phone where you left off on your laptop.
On those services, "send" is no longer the moment your text leaves the device. That has already happened, bit by bit, while you were typing. This varies by provider and is rarely prominent in the terms, so if it matters to your assessment, ask the vendor rather than assume.
Everything else watching the same page
The largest category in practice, and the least discussed.
A browser extension with read access to the page can see what is on that page. That is not a vulnerability; it is the permission the extension was granted when it was installed. It covers translation helpers, writing assistants, screenshot tools, password managers and the extension somebody installed two years ago for one task and has not thought about since.
So the question is not whether extensions can see the field, but which ones are installed and who approved them. See why browser extensions are AI tools too.
Two cases deserve a special mention:
Third-party writing assistants. The checker built into the browser runs locally. Standalone assistants that improve grammar and tone typically send your text to their own servers to generate those suggestions. That is a second processor, with its own retention and its own jurisdiction, stacked on top of the AI tool you were already typing into.
Mobile keyboards. Keyboard apps with predictive text and cloud sync learn from what you type. On a work phone running a personal keyboard app, that is a processing operation nobody has assessed.
Why this is more than trivia
For a DPIA it matters because the processing chain is longer than the paperwork suggests. You assessed the AI vendor, yet there may be three parties in the path: the extension, the writing assistant and the assistant you actually meant to use.
Day to day, the conclusion is more reassuring than it sounds. The input field is not a waiting room where text does not yet exist. It is the first place the text exists, and at the same time the last place anyone can change it without having to undo something somewhere else.
Which is exactly why the moment of typing is the interesting one. Not because it is where most things go wrong, but because it is the only point at which the text is still yours.