Cleanup\Refactor: Refactor PlaceholderListDatabase to eliminate the call to WriteAllEntriesAndFlush

From discussion in #408:

@wilbaker would it be possible and safer to have a method that takes a delegate like
Func<List<PlaceholderListDatabase.PlaceholderData>, IEnumerable<PlaceholderData> updatedPlaceholders>
Then we could hide the fact that these need to be tied together by having the method be something like

void UpdatePlaceholders(Func<List<PlaceholderListDatabase.PlaceholderData>, IEnumerable<PlaceholderData> updatedPlaceholders> updateWork)
{
    List<PlaceholderListDatabase.PlaceholderData> placeholders = this.GetAllEntries();
    this.WriteAllEntriesAndFlush(updateWork(placeholders));
}

And make the 2 methods private.

Search for PlaceholderListDatabase, GetAllEntries, and WriteAllEntriesAndFlush, then inspect the callers that coordinate placeholder updates. Introduce the proposed update method, make the two existing methods private, and verify that all placeholder-update callers still compile and preserve the read-update-write-and-flush behavior.