Some of these databases have lists of plays with where they're published, but many include the full text of plays.
To find plays as ebooks in CLIO, try a search for online books. You can always limit by language, publication date, and put in a search term (e.g., "monologues") to help narrow your search
Plays are shelved with literature, which means they're normally broken down into the nationality of the author. A selected list of Library of Congress literature subject headings:
Search Tip: When browsing or searching titles, remember that plays are often collected in anthologies. Try searching the work’s title as a keyword. You may also wish to consult a reference source such as Ottemiller's Index to Plays in Collections, or look through other drama indexes in CLIO.