Bug: Newly created projects need browser refresh before they appear in the project dropdown.

[abigailbramble]

Bug Description

Bug description

Newly created projects don't appear in dropdown unless the page is refreshed.

How to reproduce

1. Click the current project name in the breadcrumbs to open the dropdown
2. Click the "New Project" button
3. Enter a project name in the dialog box
4. Click the "Create Project" button in the dialog box
5. Click the current project name in the breadcrumbs to open the dropdown again (once the dialog box closes)
6. Observe the newly created project is not in the list
7. Refresh
8. Click the current project name in the breadcrumbs to open the dropdown yet again
9. Observe the newly created project is in the list

Project creation should not require a refresh to select it from the list.

Additional context

https://posthoghelp.zendesk.com/agent/tickets/20373

Debug info

No response