Change menu glyph from bars (hamburger) to user (account)
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.
Eric Young commented
This would be a welcome improvement. We currently have the bars and the "My Account" button shown to ensure a user can find "My Account" the icon change would improve this and maybe we would then not display the "My Account" button.