If I want to move things between them, I should open the clipboard manager and manually move an individual item, or bridge the two clipboards for a specified time, after which they go back to being isolated.
Is that sensible/practical?
All of my AutoHotKey triggers are off of the right control since I noticed a long time ago that I never use it regularly. In the old days (~2004) I would use it to write HTML. Hitting right Control+a for example would surround the text with an <a> and have logic for @ or http: etc - or hitting right Control+l would surround a list of items with <ol><li>. These days I have very few macros, the most useful one being code that will "type" what's on my clipboard rather than paste it which is useful for places that don't allow pasting.
>^v:: SendRaw %clipboard% Return
When an application makes data available in the clipboard, it's a free-for-all for every other application. The clipboard manager would have to race other applications to make a copy of the data, and then empty the OS clipboard.
APIs also may not allow making decisions based on which application requested the clipboard. It's possible to do in X11, but not Windows.
This goal could be achievable by intercepting the OS clipboard API. On X11, this can be done by MITM-ing the connection to the X server - https://github.com/CyberShadow/hax11 does this, and already has one clipboard-related security feature (disabling the selection mechanism). On Windows, the best bet is probably global DLL injection and API hooks, but applications can "opt out" by running as a different user or requesting a higher integrity level.