"Sweeney Todd" does not have an overture - just a short "Prelude". And no production I have ever seen of "Into The Woods" has had an overture either. In fact, few Sondheim shows have an overture, the major exception being "Merrily We Roll Along", which has a wonderful overture - and "A Little Night Music" has an overture which is sung by the Liebeslieder singers.
Most "older" musicals had overtures (e.g. "South Pacific", "The King And I", "My Fair Lady", etc.) while most "modern" musicals do not, often preferring to ease into the dramatic content of the show more naturally.
THEATRE 2020: CURTAINS**** LET'S HEAR IT FOR THE GIRLS***** WICKED***** KEITH RAMSAY TAKING NOTES WITH EDWARD SECKERSON***** KAYLEIGH MCKNIGHT CONCERT***** RAGS***** ON MCQUILLAN'S HILL** DEAR EVAN HANSEN***** THE JURY***