The Original Series had a Romulan Bird of Prey
No, it didn't.
It had a Romulan vessel in "Balance of Terror" and "Deadly Years" that was known as... "the Romulan vessel". Or, alternately, as "the enemy vessel".
"Bird of Prey" is a designation only ever applied on Klingon starships in the episodes and movies.
thereby giving the Klingon’s cloaking technology in which they never possessed before
We were never exactly told that Klingons wouldn't
know how to become invisible. Lately, ENT has given us "retroactive precedent" that they did. And an invisible ship is a good explanation to how the Klingons were able to surprise the war-ready Enterprise
in the teaser of "Errand of Mercy"...