Web gui should indicate whether I’m logged in

[AA5B]

Requirements

• This is a feature request and not a bug report. Otherwise, please create a new bug report instead.
• Please check to see if this request (or a similar one) already exists.
• It's a single feature. Please don't request multiple features in one issue.

Describe the feature you'd like

When I’m using Lemmy from my mobile browser, I’m frequently logged out (possibly bug #1953). However there is no clear distinction between whether I’m logged out vs just have no unread replies

in the web gui for Lemmy, in the upper right corner is a hamburger menu and notification icon. If there are unread replies, you’ll see a notification count and know you’re logged in. However if there are no notifications, then it’s unclear whether you are logged in.

Related to enhancement #2282 - I understand the privacy issue so maybe displaying username isn’t the answer but something should be there