First officer's log, Stardate 2122.4. A Federation probe, the Angelo-1, has overheated and shut down. Which, unfortunately for this probe, means it has now drifted across the demarcation line and right into Klingon territory. Starfleet has ordered Enterprise to recover it. Only Enterprise itself poses too great a risk of detection. And detection could mean restarting a very cold war. So, Captain Pike has tasked me with retrieving it. It's a delicate mission in an unusual part of space, and also my first as a newly promoted commander.

Shart Carbuncle — 6:20 AM
That line in the opening monologue about the risk of “restarting a very cold war” was unforgivable. Such poor command of the language.
How many eyeballs does a script like this go past?

[someone asks what my problem is... hold onto your ass, because I’m gonna tell you, bucko!]

it’s a linguistically incoherent line
if it was “colder” than an original recipe cold war, that would mean it’s even less likely to turn into open conflict (hot). But also, she’s talking about restarting it, which makes it sound like they’re actually in a cold war already, as a cooling off from an existing war....
god it’s just so bad
If the implication was meant to be that it’s currently a “very cold” war, as in it cooled off so much that it’s basically nothing to worry about, but the current situation could raise tensions, then it’s still extremely awkward to put it that way.
it comes across like mad libs

The line reading doesn’t help, but I don’t think there’s a good way to do it.
We all say and write dumb stuff that doesn’t make sense sometimes, but nonsense like that shouldn’t survive a professional writing process.
new trek is riddled with technically bad writing like this.
And not in a Mamet-esque naturalistic way, where it adds to the reality to have characters “talk wrong.”
It’s just clear that the writers don’t have a good handle on English.

It happens with all of the characters, whether they’re in a casual conversation, or doing Vulcan science stuff, or official military-adjacent commands, etc.
I’ll end this rant (sorry) with one example, which I believe was from the very first episode of SNW. Before leaving the bridge, Pike handed off control of the bridge to another officer by saying, “You have the comm.” The word is “conn.”

Now, I don’t expect everyone to know naval jargon, but if you are writing a submarine show that uses naval jargon, it is your fucking job to learn it.

Maybe that was an actor slip-up, but old trek shows (or any show that was being made carefully) would have either corrected it on the spot, or done a pickup, or looped it.
The people making this show simply don’t care.
I know these seem like super nitpicky issues, but it’s that same carelessness that leads to larger issues, like the gaps in logic and brutally shoehorned expository conversations.

“Una, you always do the right thing. I’m telling you this, because it’s kinda the theme of the episode I guess? I bet it’ll be tested within the next 40 minutes. Anyway, here’s why everything is black and white, I guess we forgot to talk about it before we got here.”