Problem: the cookie details do not update in console. In order to show the correct cookie details you can click on (e.g.) another storage option and then back on previous one.
The cookie details would automatically update on Friday 27 Nov 2020. The recent update broke it. Current version 83.0 (64-bit) on Ubuntu.
Seems like nobody responded so far. I’ve just created a fiddle to test that and I cannot reproduce that issue (using Firefox 86.0.1 on Windows 10).
The test case sets a cookie to a random value every five seconds and I can see the value getting updated within the Storage Inspector.
Do you still have that problem? Note that there is a reload button at the very right of the toolbar to update the panel contents. That can also be used as a workaround instead of selecting another storage and then the previous one again.
Note that there are also known issues using the Private Browsing Mode and when Fission is enabled, causing cookies or even hosts not to appear at all.