Set the Site Branding Logo to the Admin Console Branding Logo

When we do a deployment, the release manager will upload the latest release logo to the admin console.  We are moving towards using sites and would like to have this logo updated for each site as well, but the release manager does not want to change any design time objects, which the logo is tied to.

We do not have any statically hosted web logo at the moment.

Is there a way to get the logo that is used in the Admin console by expression so it can be shown in each site?

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