It appears the origin of the modern meaning is from the figurative meaning of skeleton. It appears that there is no relation between the two usages. Barebone Parliament was used more as term of criticism:
The mere essentials or plain, unadorned framework of something, as in: This outline gives just the bare bones of the story; details will come later.
- This phrase transfers the naked skeleton of a body to figurative use. [c. 1900 ]
(The American Heritage® Idioms Dictionary)
The Barebones Parliament refers to a specific historical event in the 17th century and was used as a expression of criticism:
Barebones Parliament, also called Little, or Nominated, Parliament, (July 4–Dec. 12, 1653), a hand-picked legislative group of “godly” men convened by Oliver Cromwell following the Puritan victory in the English Civil Wars. Its name was derived from one of its obscure members, Praise-God Barbon.
The nickname of Cromwell's Parliament of 1653, from one of its members, Praise-God Barbon, an Anabaptist leather seller of Fleet Street. It replaced the Rump Parliament, but was itself dissolved within a few months.
(Oxford Dictionary - Enciclopedia Britannica)
- In July 1653 Barebone was appointed to sit in the Nominated Assembly, a body set up after the expulsion of the Rump Parliament by Oliver Cromwell. The Assembly, whose members were chosen by Cromwell and the Army Council instead of being elected, soon became known as Barebone's Parliament to its many critics, Barebone proving a likely target due to his name and his apparently humble origins.