[Menu bar] add Project affiliations

[christinerogers]

Goal: in the top menu bar, add a way for users to see their project affiliations -- similar to how they can currently see their Site affiliations.

To get started: copy the Site affiliation drop-down, adapt it for Projects
Post a screenshot in the PR when ready.

Later once we see how it looks in the PR review process, if it takes too much space on the top menu bar we may discuss options for saving space (maybe combine the 2 dropdowns or find another solution)

Assigning to @NadaElmasry for a first GSOC issue late May
cc @laemtl mentor

[christinerogers]

@NadaElmasry to push draft PR before Sept. 3, screenshot

[christinerogers]

Waiting on push from @NadaElmasry linked to this issue