What about the Prime Directive with Capellan?

There is no problem with the Prime Directive.

McCoy had been with a medical team from the Federation, offering medical assistance to the Ten Tribes, at an earlier date than "Friday's Child".

Obviously the Prime Directive was not in full force at the time when that medical tream visited. That means that Federaton and stafleet knew that the Capellans had been contacted by someone before the medical team visited, and knew about life on other worlds, and thus the parts of the Prime Directive about informing people about other worlds no longer applied to the Capellans.

Possibly Capella IV had been conquered by the Klingons or the Romulans and had been liberated by the Federation during a war with the Klingons or the Romulans. Maybe a planet had conquered the Capellans and then had to grant independence to Capella IV when it joined the Federation.

Only the parts of the Prime Directive about not interfering with the natural development of Capellan society should have applied to Capella IV.

Of course any dealings with the Capellans could be considered interfering, to a greater or lesser degree, in the natural development of their world. Possibly Capella IV was in the Prime directive category of planets where peaceful contacts and trade, possibly leading to unplanned changes in their social development, were allowed, but no deliberate attempts to change their society or forceful interference were permitted.

Or maybe the Prime Directive was bent a bit to negotiate with the Capellans because the need for topaline was so great. Necessity is often used as an excuse to ignore rules and ethics.

To me the big problem with negotiating with the Ten Tribes of Capella IV is the idea that they rule all of Capella IV. A planet large enough to be habitable for humans would be vast. It is hard to believe than ten tribes can be the entire population of intelligent beings on a such a vast planet.

Maybe the word translated as tribes should have been translated as nations, or warrior hordes, or cultures, or something else which implies numbers larger than those of tribes, which implies no more than a few thousand people per tribe.

It seems extremely improbable that the Ten Tribes can rule the entire land area of Capella IV if their only mode of transportation is walking.

If they can send messages and orders by horseback then they could operate a vast empire like the Roman, Achaemenid, Chinese, Mughal, etc. empires. But if walking or sometimes running is the fastest way to send information and orders, the High Teer of the Ten Tribes should only be able to rule for a few hundred miles in any direction from his capital.

Possibly the capital of the Ten Tribes is a vast tent city and army encampment constantly on the move from place to place to reminde everyone the High Teer is their ruler. Much like the capital of the King of Kings of Ethiopia was a moving tent city during the Middle Ages and until the city of Gondar was founded in about 1600. So it would be plausible for the High Teer to rule a land as large as Ethiopia was about 1500, which was a lot smaller than modern Ethiopia if I remember correctly, so maybe about 500,000 square kilometers or 200,000 square miles.

If the Ten Tribes were horse riding nomads, and their lands happen to be bordered on every side by the lands of sedentary civilized peoples, then maybe when the first High Teer united the Ten Tribes they could have conquered the civilized lands bordering their land one by one, much like the Mongols after Genghis Khan united them. And if those civilized lands bordering the ten tribes reached to the edges of a continent that was smaller than Eurasia, they might rule that entire continent. And if that continent was the only landmass occubpied by Capellans, the Ten Tribes would rule all of the Capellans and the High Teer would be ruler of all the Capellans of every tribe and culture.

But if walking or running is the fastest way to send orders or information, the High Teer would probably be limited to ruling a much smaller area than the Mongol Empire at its height.

It is true that the Inca Empire stretched for over 3,000 miles from north to south using runners for communications, but it was rather thin in an east-west direction.

Its area is listed as 2,000,000 square kilometers or 770,000 square miles in 1527, which is quite respectable, but only one twelfth, or 0.0833 of the size of the Mongol Empire, and only 1.48 percent of the world.

https://en.wikipedia.org/wiki/List_of_largest_empires[1]

My best guess is that the Capellans originated on a small continent or large island with large low areas and relatively small highlands. During the glacial periods, the large flat low areas are above sea level, and there are large areas for the Capellans to occupy. During interglacial periods the sea levels are higher and the lowlands are flooded and the Capellans can only live in the small area of the highlands. TOS happens during an interglacial period when the Capellans are restricted to living in the small highland area. And the Capellans have never developed water craft capable of reaching islands or other land masses, and so have never settled other lands on Capella IV.

And apparently the inhabited highland area is small enough to sometimes be united by a culture which doesn't have riding animals, and so it should be no larger than the Inca Emire (2,000,000 square kilometers or 770,000 square miles) and possibly much smaller.

And today I wonder whether the Ten Tribes do rule all of Capella IV. Possibly, repeat possibly, the Ten Tribes don't rule all of Capella IV, but topaline is only found in their territory. Negotiating with them to mine topaline would be the equivalent of aliens from other space negotiating with a country on Earth such as Russia or Liechtenstein for mining rights for something only found in that country. Except that in the case of Capella IV theee woudln't be any United Nations or other internaitnal organizations or treaty allies or whatever to demand a share in the deal.

As far as I know there is no rule that would force the Federation to negotiate with people for the right to mine on land thosee people don't own or rule. If that was the rule the Federation would have to negotiate with everynoe in the universe to mine anything anywhere.