For a period, ESET's "Banking and Payment protection" (as it was called) would create a separate desktop shortcut. When you launched that shortcut, it would open your default browser in the secure, green-bordered mode, and that mode was intended to be used specifically for banking and financial transactions. This was a clear and intentional way for users to know they were in a protected environment.
However, ESET has since changed the default behavior of this feature. Now, with the "Secure all browsers" option enabled by default in many of their products, the secure browsing mode with the green border automatically launches for all supported web browsers. This means that the green border is present whenever you're using a web browser, not just when you're on a banking website.
This change was made to provide a more comprehensive and continuous layer of protection, but as you've noticed, it can also lead to the green border being on all the time, even when you're not doing anything financial.
ESET simply evolved the feature to be more proactive and to secure a wider range of online activities by default. You can still get back to the old behavior by disabling the "Secure all browsers" setting in your ESET product's advanced setup.