Did you bother to actually watch any of them? I ask because
Friday's Child deals with the Federation making a mining agreement with a pre-warp civilization. The reason they can do this is because the Klingons already contacted the inhabitants, so sad inhabitants know of alien life on other worlds thus the prime directive doesn't apply; thus the Federation can make a mining agreement with this primitive culture.
In A Private Little War, we learned that the prime directive isn't always automatically applied. Again we have a primitive civilization where Kirk lived among the primitives, and revealed himself and his origin to one of them while he did the survey to see if the prime directive applied, and ultimately the Federation Council decided it did based on his report:
http://www.chakoteya.net/StarTrek/45.htm
.
.
.
So yes in the 23rd century, the Federation does a planetary survey where possible to determine if the prime directive should be applied or not. It's not a blanket policy.
In
Elaan Of Troyius, the civilization involved is space fairing, but doesn't have Warp Srive technology/capability. The only reason the Federation is getting involved is because the both the Federation and the Klingons claim the area of the system resides in: and at the start the Federation see some political advantage to annexing this star system. In the end they find out the reason the Klingons are so interested is because both planets have Dilithium Crystals that to the inhabitants are of little value because as Elon herself states: "...they are common stones..."
^^^
And it's possible Federation planners may have known this as well, and that's the reason they are getting involved with the situation in the system even though the cultures of both planets are pre-warp.
So again, if the 23rd Century Prime Directive was like you claim in the 24th century; the Federation shouldn't even be doing such surveys, making mining treaties with primitive cultures, or getting involved with the Affairs of pre-warp cultures; yet in the three episodes above they definitely are.
As for
Bread And Circuses , here's a transcript of the exchange between McCoy and Spock that I was talking about:
http://www.chakoteya.net/StarTrek/43.htm
^^^
And the reason the Prime Directive is in full force here is because the civilization is both pre-warp, and has no knowledge about life on other planets.
Bottom line: there's plenty of evidence in TOS to show that the Federation Prime Directive of the 23rd century is quite different from the Federation Prime Directive of the 24th century.
So as far as this episode of Strange New Worlds, as the events in the episode take place in the 23rd century, that's the version of the Federation prime directive that is being applied in the episode. Because the civilization is both warp capable, and has knowledge and contact with alien life of other worlds, the 23c Federation Prime Directive doesn't apply.
Pike even States he'll report this incident to Starfleet and the Federation Council, but both he and the planet's leader know that the Federation will most likely not do anything because the planet is not a member of the United Federation of Planets, and they don't see a valid political or other advantageous reason to become involved with the situation.