fieroscotty,
The bank’s purpose in throwing the pop-up notification about your session timing out, is probably designed to steal your focus?
If you wrote about the issue - to the bank - would they not say that? And, advise you to “simply log out” when you intend to be focused elsewhere and wish to not be disturbed?
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Meanwhile, you might learn about the Brave Browser Developer Tools >> Network. How to get to those tools and what to see:
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Try to find what process, and what server (of the bank, or a 3rd party, assigned to the task of producing that pop-up) . . . are the cause.
You might convince a member of Brave Support (“fanboynz”) to gin up an AdBlock script addition, that would block the specific process . . . and that little script-thing, you would then add in the “Custom Filters” box, at the end of:
brave://adblock/
An example of “fanboynz” work: