I ran into the same issue. I was able to find my insert key, and it did not appear it was functioning.
It appears that google chrome and more specifically gmail only 'enable the toggle' of overtype mode in certain text boxes, however, this overtype mode once enabled is applied to other text boxes. So....
If your Insert key works (i.e. works in word or excel given enabling the key) but you are struggling in gmail. This could be the issue:
COMPOSE a new message
go down to the BODY of the new email (not the subject) and my insert key is functional there, toggling Overtype on and off. If I toggle overtype ON and then trash that message, overtype is still enabled for various parts of gmail. However in the search bar, or even the subject line of a message, the insert key is not enabled, meaning it can't be toggled off.
reply to a message, or COMPOSE a new message, go to the body of the email, and the insert key once again can toggle Overtype on or off.
Hope this helps someone.