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It seems I found the information that answers my question at least partially (see below). It might change when the shuttle starts operating (June 19, 2021), but then I hope it will be updated on the website where I took this information from.
Service is currently operated every 10-20 minutes on weekends and holidays only. Service to Muir Woods from Pohono operates from 8:30 am to 3:00 pm and return service from the Park operates from 10:30 am to 6:00 pm (or earlier depending upon Park closure times).