As I understand it, the office of state governor is a holdover from the American colonial period.
Did the powers and responsibilities of a governor in America change substantially in the period from 1776 to 1850?
Similarly, did the powers and responsibilities of a governor in a British colony like the Cape Colony, Sierra Leone, Hong Kong or Bermuda change in that same period?
Was there a divergence in how these institutions interacted with Federal authority or the authorities in London?
Taking a step back, is this question that easy to answer? Is there too much variance between what authority governors of the various states had to make a coherent case? Were the powers of British governors similarly as varied?
I don't know about Hong Kong, Sierra Leon...For the 13 North Atlantic colonies, initially governors were either appointed by the King ( royal colonies) or selected by owners of the company that created the colony ( proprietary colonies). New York was a royal colony, Boston Bay, Plymouth , and Maryland were proprietary. Over time ( by 1776) they all essentially became royal colonies. The powers of the governor as head administrator of the state government could be said to stay about the same, but he went from governing on behalf of the king to governing on behalf of the citizens of the state, the majority of whom elected him. That, of course, is a very big change.
But you might say that the Boston Bay Colony was ahead of its time, in that it was able to gain the right to govern the colony within the colony for a while in the 17th century. Most of the other proprietary colonies had their companies back in England. This meant that Boston Bay could do a lot more of what it liked. Other proprietary colonies of the 17th c. typically had constant contention between colonists asking for more money and supplies and proprietors back in England asking for a return on their investment.
During the Articles of Confederation period the inter-state government was very weak- just the Continental Congress, which had very little power and attracted few people with any ambition. Governors during this time were the most important political figures, like George Clinton of New York. Once the Constitution was ratified, that of course changed. But some of those changes happened over time. New York , for example, gave Robert Fulton a monopoly patent for his steam boats, New Jersey did not, and this became the legal case that gave the Federal government power final say over any interstate commerce. Even in the 1980's, there was a question as to whether governors still had final authority over their states' national guard units, when Reagan wanted to use them in his war on Nicaragua.