Anyone remember the James Blish adaptations of the original series episodes? Now all of them were far too short, especially in the case of "Balance of Terror".
But Blish's written version of "Balance of Terror" IIRC suggests that the Federation outposts and the Romulan Neutral Zone actually surround the home solar system of the Romulans.
If this was true, then it is obvious how the Bird of Prey could've attacked using only sublight impulse engines and also explains why there was a comet with a tail near the Neutral Zone as comets can only have tails when near a star.
But the problem then is how can the Romulans be one of the major bad asses of the galaxy if their "empire" consists of only one solar system.
The official TOS warp factors were much too slow for some of the travel times in TOS. Thus there are many theories that seek to explain that and other mysteries and contradictions about space travel in
Star Trek. One theory is that some interstellar travel in
Star Trek. is done by using warp drive to travel across space from star to star, and some other interstellar travel, especially long distance travel, is done by traveling through some type of space warps or wormholes from star system to star system. A ship would use the space warps to disappear from one star system and instantly appear in another, tens or hundreds or thousands of light years away.
So the Romulans would have been expanding both by using some FTL drive and by going through space warps to distant star systems. And a map of the Romulan Star Empire would look like a bunch of spheroids or ellipsoids scattered through 3-D space. And during the Romulan War the Romulans in the space around Romulus and Remus were driven back star by star until they had only the Romulus/Remus system left and Earth was preparing to attack and destroy the capital worlds.
So the Romulans negotiated a treaty via radio giving up all their stars systems around their home system, and establishing a spherical shell neutral zone around their home system. But the treaty didn't force the Romulans to give up the star systems they reached through space warps from their their home solar system. It permitted the Romulans to keep on expanding from the stars systems they reached through those space warps. But whenever Earth, or later the Federation, expanded through the space warps and colonized or annexed a planet sufficiently near to a Romulan planet, they had the right to notify the Romulans and demand that the Romulans agree to the creation of another neutral zone segment around that Romulan star system or group of star systems.
And now the Romulan Star Empire looks like a bigger bunch of spheroids or ellipsoids scattered through 3-D space, some with Neutral Zone segments around them and some without.
Or maybe the treaty requires the Romulans to send by subspace radio the coordinates of every star system they annex and colonize through the space warps, and agree to not expand through space from star to star using FTL space drive but only expand by travelling through the space warps and only annexing each single star system around each space warp.
Note that in "The Deadly Years" a segment of the Romulan Neutral Zone is near Gamma Hydra (Hydrae) about 133.8 light years from Earth, and in "Whom Gods Destroy" Spock mentions a Romulan ship destroyed near Tau Ceti, about 11.9 light years from Earth. It would certainly be a lot safer for Earth if there were two separate and small Romulan Neutral Zone segments near Tau Ceti and Gamma Hydrae instead of one huge Romulan Neutral Zone segment stretching from Tau Ceti to Gamma Hydrae.
As late as the era of TNG, DS9, and Voyager, there is still a Romulan Neutral Zone, but the Romulan Star Empire is a major power in the region near Earth, providing vital reinforcements to the Federation and the Klingons when they were loosing the Dominion War and turning the tide.
As early as "Balance of Terror" there was a strong indication that even though the Romulans can't pass through the Neutral Zone surrounding their home system, they rule many other star systems far beyond it.
COMMANDER: Danger and I are old companions.
CENTURION: We've seen a hundred campaigns together, and still I do not understand you.
If they have seen a hundred campaigns together, probably most or all of them after the Romulan Neutral zone has been established around Romulus and Remus a century before the episode, they have probably been fighting and conquering in space battles in distant star systems tens, hundreds, and thousands of light years from Romulus and Remus.
I have considered the possibility that maybe the Romulan Neutral Zone covers the mouth of a wormhole or spacewarps leading from near the center of the Federation to Romulan Star System. So Starships travel through the wormhole or space warp to the Romulus system and emerge from the mouth and bring supplies to the outposts and patrol between the outposts looking for any Romulan attempt to try to reach the moth of the wormhole or space warp.
If Romulan ships can cruise at warp factor 6, 216 times the speed of light, and if the Romulan star system is 2,160 light years from the main worlds of the Federation, it would take a Romulan invasion force 10 years to reach the main worlds of the Federation from the Romulus system, which may be too long for the Romulans to attempt.
In "Redemption Part II" the Romulans used cloaked ships to send vital war supplies to the part of the Klingon Empire controlled by the Duras faction, since apparently Gowron's faction controls the Klingon manufacturing planets and other sources of supplies. Since proof of Romulan support would turn all Klingons against the Duras faction and cause involvement by other powers, Captain Picard leads a Federation task force of 23 ships to operate a tachyon detection grid along the border, that will detect any cloaked Romulan ships trying to cross.
One would expect that the Romulan-Klingon border might stretch for hundreds of light years in each direction and cover tens of thousand of square light years. But the 23 Starfleet ships take up a disc shaped formation that seems to be only a few miles in diameter. how could that cover the entire Romulan-Klingon border?
Maybe there is a neutral or unclaimed star system A near the Romulan border, and a neutral or unclaimed stars system B near the Klingon border, that could be hundreds or thousands of light years apart, but there is a space warp system A and System B that connects them and allows almost instant travel between system A and system B. And maybe Picard's fleet flew into the space warp between system A and system B and set up a detection grid covering the entire diameter of the space warp, which might be only a few miles.
Maybe it would take many years for the Romulans to get the supplies to the Duras faction if they can't travel from system A to system B, which would be too late for the Duras faction that needs the supplies immediately.
No doubt there are problems with this theory, but it seems that any other theory would have much stronger problems.
That is my explanation for how the Romulans have a mighty space empire even though their home solar system is surrounded by a Neutral Zone they cannot cross.