"Balance of Terror" establishes what Starfleet knows about the Romulans a decade after Discovery.
Captain's Log, stardate 1709.2. Patrolling outposts guarding the neutral zone between planets Romulus and Remus and the rest of the galaxy, received emergency call from outpost 4. The U.S.S. Enterprise is moving to investigate and assist.
KIRK [OC]: This is the Captain speaking. In our next action, we can risk neither miscalculation nor error
KIRK: By any man aboard. Listen carefully. Science Officer.
SPOCK: Referring to the map on your screens, you will note beyond the moving position of our vessel, a line of Earth outpost stations. Constructed on asteroids, they monitor the Neutral Zone established by treaty after the Earth-Romulan conflict a century ago.
SPOCK [OC]: As you may recall from your histories, this conflict was fought,
SPOCK [OC]: By our standards today, with primitive atomic weapons and in primitive space vessels
SPOCK: Which allowed no quarter, no captives. Nor was there even ship-to-ship visual communication. Therefore, no human, Romulan, or ally has ever seen the other. Earth believes the Romulans to be warlike, cruel, treacherous, and only the Romulans know what they think of Earth. The treaty, set by sub-space radio, established this Neutral Zone, entry into which by either side, would constitute an act of war. The treaty has been unbroken since that time. Captain.
KIRK: What you do not know and must be told is that my command orders on this subject are precise and inviolable. No act, no provocation
KIRK [OC]: Will be considered sufficient reason to violate the zone. We may defend ourselves,
KIRK [OC]: But if necessary to avoid interspace war,
KIRK: Both these outposts and this vessel will be considered expendable. Captain out.
So as far as starfleet knows, no ship has crossed the Neutral Zone in either direction for 100 years since the Romulan War. Apparently there has been no contacts by subspace radio since the war, either.
KIRK: After a whole century, what will a Romulan ship look like, Mister Stiles? I doubt they'll radio and identify themselves.
STILES: You'll know, sir. They're painted like a giant bird-of-prey.
Stiles doesn't know that all Romulan ships will always be painted like a giant bird-of-prey. It turns out they still are in his time, but a century later in the time of TNG they are not. So Stiles was only guessing about that.
In in the era of Discovery, a decade earlier, if a ship crosses the Neutral Zone in either direction and is detected, a war will start that didn't start in the alternate universe of TOS. If the crew of Discovery have any Romulan contact they will be obligated to report it to Starfleet Command.
So I can imagine that crew members of Discovery might visit a busy spaceport on a new contacted planet and someone might point to a tentacled alien and say: "That's the weirdest alien I ever saw." and someone else might say: "It sure is. I wonder if it could be a Romulan."
And that is about all the writers of Discovery can do with Romulans.