Spoiler
On route to at the planet Archer was making first contact with, Spock briefs Pike and Lt. La’an Noonien-Singh about the planet, noting that the planet is not ready for warp drive technology. Developmentally, they are about at 21st century Earth's level. He also points out the oddity if they are developing it as a weapon, comparing it to nuclear technology. Apparently every race develops the nuclear bomb before developing reactors, where as warp technology is always developed as a drive rather than as weapons. They debate if General Order 1 applies or not, since it would seem they may have been given Warp technology. Arriving, they find the Archer abandoned in orbit, and note the warp signature coming from the planet seems odd. Apparently the Archer only had three crew members (even though a starship in this era shouldn't be able to operate with only 3 crew members) that must have all beamed down to the planet. The Enterprise is attacked by plasma torpedoes, which are harmless against their shields. Pike notes these weapons are 21st century level technology (despite the Romulans used this type of torpedo in the 23rd and 24th centuries). What ever happened to First Contact being a long process of careful observation and study up until the species achieves warp flight? The Enterprise crew are completely confused by this planet's technological development, when they really shouldn't be if First Contact's guidelines were being met. Needing to investigate, Pike, Spock and Noonien-Singh (it feels so odd typing this name with out it being Khan) go to sick-bay where Nurse Chapel gives them an experimental gene treatment to alter their appearances in order to blend in with the natives. Although she's concerned about Spock's unique genetics, warning him it'll probably wear off quickly for him. After beaming down, they quickly locate the building the mission Starfleet officers are in, but they are deep underground, so they'll need them closer to the surface to get a transporter lock.
After some difficulties, the three are able to break out Una and her two crewmates. She explains to Pike that this planet is less than a lightyear from where Discovery jumped to the future and the battle with Control took place. This planet, was able to see everything with their telescopes and developed warp technology as a direct.... This is dumb. Even if they could see the space battle from this planet, how would they be able to figure out the ships were powered by a matter/antimatter reaction? They wouldn't have seen a warp core or any of the internal workings of the ships to have been able to figure anything out about how they work. At any rate, Pike decides to ignore General Order 1 and everyone except Spock (having his disguise wear off completely at this point) and himself beam up to the Enterprise. They're taken to this country's president where he warns her not to use warp technology as a weapon. She explains her position with their neighbor country as whoever has the bigger stick wins. Pike decides to show them he has the bigger stick by having the Enterprise drop down to hover above the city. The two leaders get together to discuss the arrival of the aliens, and Pike beams down again, showing them some of Earth's history. He explains that second Civil War developed into the Eugenics Wars which then became World War III (as I mentioned with the Picard finale, looks like these writers are retconning the Eugenics Wars to take place after 2024, and here they reveal it developed directly into World War III. But not only that, apparently the United States had a second Civil War that kicked all of these wars off? That's never been mentioned before...). He explains that after Earth nearly wiped itself out, they learned to work together. And so he asks them if they really want to wipe themselves out, or if they want to join the Federation.
Back at a starbase, Admiral April is not happy with how Pike handled the situation by completely ignoring General Order 1. However, because this world developed warp technology based on an event that has been classified, it has created a loophole. They can't acknowledge how this planet developed warp technology because it would mean exposing Discovery's time jump as well, so the whole thing is conveniently going to be ignored. They're also renaming General Order 1 to the Prime Directive, which Pike says wont catch on. I guess this is to explain why it was somewhat inconsistently named in TOS. As an aside, during a discussion with Lt. Noonien-Singh about surviving a Gorn hatchery planet, Pike asks if she knows the story of why this starbase has a forest, and explains Earth had sent seeds into space so that they could rebuild the ecosystem, only when Earth was ready to rebuild, the forest was too large to bring down to Earth... Why did they grow the seeds into a whole forest in the first place? Or at least regulate their growth? Anyway, Enterprise finishes its crew rotation (adding a chief engineer and Sam Kirk, James T. Kirk's brother) and maintenance. With this mission reinvigorating Pike, he's fully ready to return to duty as the Enterprise heads out o continue its mission of exploration.