Ok here are some options.
1. change login button
go to admin -> site texts
then type “Log in” in the top filter field. A list will show up and it should be the one at the top called js.Log_in
- edit that one
result (on mobile):
2. welcome banner with cookie control
If you use the Versatile Banner component and make your own banner, there are cookie-related controls for how it behaves for users. Alternatively, you can fork it and make your own custom banner.
3. hamburger menu replacement
In a new or existing local theme or theme component, click the “Edit CSS/HTML” and go to the “Head” tag and put this:
<script type="text/discourse-plugin" version="0.11">
api.replaceIcon('bars', 'user');
</script>
result:
I don’t believe that pointing it to a modal is possible without some custom programming work. Does that mean you want to hide the whole sidebar menu for anon users? if so, this theme component has that functionality.