@Vlad A tagging system solves the same basic issues of current lack of closure & the need for quick information saving before working memory expires & without switching to another app & disrupting The Assistant in between. Per-thread system's advantage is obviously capturing the dialogue of both the user & the AI. This feels to me sound as an update for The Assistant's UI proper & sound.
@dps My previous comparisons to Joplin & Obsidian were made with assumption you forget what you search for, but Custom Lens with any stacks (plaintext files) of your choice + Search would indeed be very fast way to recall past information generally.
I imagine one could for example add a text stack that contains what items you own + text stack logging changes in fridge/pantry + text stack of recipes for favourite foods to Lens called Recommed Recipes. When you search for how to make favorite food, you push the Quick Answer to the recipe stack. When hungry, you open an Assistant named, say, "Food Assistant", which uses that Lens, and ask it about what food can you make right now, and it should yield a decent answer. Such food recommendations based on fridge/pantry have apps already, but nothing limits you to this single use example.
I imagine, as you understood correctly, a consistent "quick-push" actions UI across Kagi for tapping any piece of information (quick answers,
Assistant responses, whole or individual bullet points of site summaries, map objects, translations), and appending it directly into the relevant text stacks,
without having to refocus attention to it.

Why not have slightly hidden interaction (like attached example from gmail) in The Assistant, The Search, Maps et cetera across Kagi, that looks roughly identical everywhere (not mimicking Gmail in the attachment UI-wise but rather internally consistent visually & following the same HCI pattern), and allows pushing bits of information to the clipboard, sharing, or The Library's text stacks (of which bottom it would be appended to)?
@RoxyRoxyRoxy The ELI5 would be that you have sacks of different colors, onto which you can drop things. When you find an useful piece of information (via search,
summaries, or the Assistant), you would with this be able to instantly drop it to the sacks you want (one or more because information can be duplicated unlike balls) without switching to another
app & back or losing your focus. This is because you do not even need to read, say, a Quick Summary, because if you think it's "probably a work thing" you can just drop it to a work sack without looking at it. You only need a broad idea of "what type of thing this is" for any piece of information. Then, when you do get back to work, you don't need to open the sack to see what new is inside it, because you can ask The Assistant to search all of your sacks for information that might be useful given whatever problem you have ("I am trying to figure out whether A or B, can you tell me what pros & cons I have found for both earlier") for you.
If you're familiar with Zettelkasten (add cards for later reference instantly), Tsundoku (stacking books you intent to read but haven't yet), or how Da Vinci saved things to research & ideas for later by adding them to the bottom of a list in a notebook, this means the same but Kagi helps you to actually get back to whatever information you put to sacks later on instead of just hoarding it.
Edit: I now have an itch of how it feels like to be a popular scientist.