Luke Skywalker has vanished. In his absence, a mysterious Imperial remnant, known as the FIRST ORDER, has emerged from uncharted space and will not rest until Skywalker, the last Jedi, has been destroyed.

Fearing that First Order spies have infiltrated the New Republic, General Leia Organa mobilizes a covert Resistance to prevent their corruption from spreading further into the galaxy.

Convinced that the Jedi are their key to victory, Leia has sent her best pilot to find her lost brother, Luke, before their dangerous new enemy reaches him first…

This is really good. It’s a bit on the wordy side compared to your TLJ crawl however. I also wish that there was a more elegant way of communicating the First Order’s goals. I think the answer might be in making them intentionally becoming the Empire 2.0, with all associated features. That way another superweapon becomes expected and important to their identity rather than out of nowhere and unexplained. It doesn’t even have to be established in the crawl. Here’s an attempt that incorporates Luke’s last Jedi status, Jakku being in FO space, and the goal of the FO itself:

Luke Skywalker has vanished. In his absence, an Imperial remnant known as the FIRST ORDER has emerged from desolate space with ambitions to restore their fallen Empire.

Fearing that First Order spies have infiltrated the New Republic, General Leia Organa mobilizes a covert Resistance to counter their sinister influence.

Desperate to restore hope to the galaxy, Leia has sent her best pilot beyond the edge of the Republic in search of Luke, last of the legendary Jedi Knights…

I think the Resistance makes a lot more sense as an intelligence operation and propoganda outfit rather than a military operation prior to this movie, and it is the events of this movie which turn it into a small and outmatched military force.