Globals are, and have always been, user session based. This is well documented
Thank you for your post!
As coherentkris stated, this behavior for Global Fields is expected in a multi-user solution. The Global Fields are session based, meaning every user has their own instance of the field. Closing and reopening the file will count as a "New Session" and give the user a blank Global Field until it is set again.
You might see Global Fields: An Overview for more details.