SNW S1E2 - Children of the Comet. This is a tricky one because of potential predestination and the end result being an accidental major break of the prime directive. A warp capable civilization is certain that a comet must destroy a pre warp civilization and refuse to let that change. The issue is that the ship/comet wants the Federation to interfere and does not intend to hit the planet. This is all in Federation space.

Another in Federation space that is also a loose fit is LD S5E7 - Fully Dialated where the crew must recover Data’s head from an alternate reality that has fallen on a pre warp world. The loose fit here is that the only reason they count as external is that it is Purple Data who is not technically a a member of this realities Federation and thus an outsider.

Lastly a decent fit but outside Federation space is Prodigy S1E7 - First Con-Tact. The crew first breaks the prime directive by making first contact with a pre warp civilization but then defends it by stopping a Ferengi from influence the civilization negatively. This is outside Federation space though.

Specifically for a new viewer who wants 3 shows that would be different and enjoyable:

TNG:

The Inner Light, Cause and Effect, Lower Decks

DS9:

Duet, The Visitor, Trials and Tribbleations

Why is your hobby more important than their hobby?

Prodigy has holoemitters on every deck and is able to reconfigure the bridge using them. It is possible but they just need a reason.

We have like three entirely reasonable shows all setup that they keep not even touching. All of them episodic, all of them able to both speak to new generations and old.

Upper Decks: Live action show with the characters from Lower Decks. Primary focus is the main characters coming to terms with the fact that they are good enough to be senior members of a crew. Continue the idea that they are the little ship that could and their missions focus around support rather than flagship or the biggest of the bads.

Prodigy 2.0: Again live action, with Ella Purnell as a captain who is super in demand and capable and would be fantastic in the role. Focus here is again episodic, when the rest of the Federation has abandoned exploration due to all the BS at the start of Picard, they are the only crew left with the charter to seek out new life and new civilizations. You have an incredibly young but capable cast and easily could bring in some heavy hitters to support them.

Legacy: This idea has floated around a ton since Picard S3, honestly its the least developed of the ideas and I’d rather see a way to roll it into one of the much better and more fleshed out ideas above. I feel like the final scene in Picard was an afterthought while both Lower Decks and Progidy it was a true capstone.