What is the ruling on opening a savings account in a usurious bank—one that does not accrue increments, profits, or usurious interest—for the purpose of using it for small online purchases, in order to avoid potential risks associated with using the main account in an Islamic bank?

You should have asked before acting and opening an account in an interest-based (ribawi) bank, as this is fundamentally impermissible and unnecessary. Islamic banks are available that provide such services, and an account can be opened with them that fulfills the aforementioned need. Therefore, close the account in the interest-based bank and replace it with an account in an Islamic bank.