Network Share as a path? I presume this might be a windows network share (which I don't have any).
Sure. SMB, AFP, NFS, SFTP, …
On Windows, you can just pull an Open dialog in any app and open \\server\share\path\to\file.txt directly that way. Behind the scenes, network authentication takes place, but \\server\share is just transparently available.
But Google Drive, icloud, OneDrive, Time Capsule, and router attached all do work as you suggest.
Google Drive, iCloud and OneDrive "sort of" work that way because they sync to the local file system anyway.
Time Capsule does not work that way at all. It mounts a network share in the background, and this causes funky issues if you use different network shares from the same machine Time Machine is on.
my watch unlock has worked reliably for a long period (like - since I set it up). Sounds like your specifics need to be reported. My watch never shows up in Console maybe part of issue?
Are you sure your Watch doesn't show up even if you leave Console running for a few minutes?
Unlock worked OK for a few months, but even when it did, I was never completely satisfied. Sometimes, it would just try to reach the Watch for several seconds, flail, then let me enter a password (why can't I enter a password while it's trying to reach the Watch, the same way I can enter a password while iPhone tries Touch ID or Face ID?). Sometimes, it would explicitly give the error message that the Watch is too far away (why doesn't it just keep retrying to see if the Watch is closer now?).
But now it just stopped altogether? Weird. And I'd love to report specifics, if only I had an idea how to find them out.