Iirc on *nix there’s a difference between inodes and vnodes that you might be able to take advantage of as well. The supervisor would create, open, and delete the directory before filling it. Holding the directory open gives it a vnode count of one and deleting it gives an inode count of zero thus making the current process the last thing to ever be able to reach the directory. You’d have to make sense of a full disk binary scan to guess what used to there if the disk wasn’t zeroed out, so encryption could help there too.

Isn't the purpose of Incognito mode to protect against tracking inside the browser? At least I haven't heard so far that its also supposed to shield data from access outside the browser.

So, wouldn't be enough to simply delete the space after closing the tab? (Or use a new, empty storage location for each newly opened tab)