The current hamburger menu opens an account menu, rather than the overall app menu. Changing the glyph from the bars glyph (https://fontawesome.com/icons/bars?f=classic&s=regular) to a user glyph (https://fontawesome.com/icons/user?f=classic&s=solid) would make it clearer that this is how you access your library account.

The menu link is located in the upper right of the app, which is a common place for an account link to go. And when you open this menu, there's already a round user avatar that appears at the top of the account menu. Swapping out the bars glyph for a user glyph would feel totally natural.

With an unambiguous link to the account menu in this position, you wouldn't need to add a redundant link to the account from the menu, thus and opening up a spot for something else.

Alternatively, the menu glyph could be configurable so a library could specify what they prefer to use.