More on when
The 'baroque' era across Europe can be considered, in very broad terms, to be from 1650 to 1750.
The seed of Italian baroque opera was germinated in 1598 by Rinuccini with music by Peri - 'Dafne'. (Monteverdi's 'Orfeo' was first performed in 1607.)
Whilst baroque theatre was developing from 1600, it was not until the middle of the 17th century that it became established, and bloomed in the decades thereafter.
In France, Corneille wrote a comedy for the actor, Mondori in 1629 although his first tragedy didn't appear until 1633. A Ballet de Cour - 'Circé ou le Balet comique de la Royne' - was first performed in 1581, however, it was not until the 1640s that opera, Italian opera, was seen in the Palais Royal. (Lully's 'Alceste', his third opera, was first performed in 1674.)
The English royal court, from 1605 - 1640, was enjoying productions by Inigo Jones and Ben Jonson, developed from the Renaissance Masque. In 1642 the theatres of England were closed by Act of Parliament. With the Restoration of the Monarchy in 1660 came the restoration of the theatre. Davenant had already been fidgeting to produce a 'Dramatic opera'. (England's first through-composed opera, 'Venus & Adonis' by Blow, was first performed in about 1682.)
Rameau's last opera, 'Les Boréades', was completed in 1764. Even later, Mozart's 'La Clemenza di Tito' of 1791 was written in the old baroque style, but by this time the attitudes of the Enlightenment were changing the style of stage presentations. The end of the era, then, was in the middle of the 18th century.
I mean no disrespect by not giving specific details of other European countries. Ancient Spanish theatre of comedy influenced early France. Sacred, allegorical dramas, Autos Sacrementales, continued into and throughout the baroque era, when they were lavishly presented in Spanish theatres.
French theatre influenced Holland. Dutch theatre, and later Italian theatre, influenced Germany. Italian theatre also influenced Vienna and the palaces of central Europe.