According to Google Help (Subscribe to someone’s Google Calendar) it can take up to 24 hours for changes to show.
Google does not disclose the actual frequency and it can vary significantly for users. It is likely they approach it in the manner of similar sync challenges, such as the behavior used to sync external non-Gmail addresses to Gmail accounts.
Google's calendar sync frequency will be imperfectly related to the frequency with which the public calendar itself is updated. If the public calendar has little to no activity when Google reaches out to sync, the syncs will gradually decrease in frequency. If a public calendar is more active the sync frequency will gradually increase.
Google has increased the "it can take up to [hrs]" value over the years but the takeaway is that at any point in time, the public calendar may not be synced regardless if the calendar is normally in sync.