Yes you refer to the Alcubierre drive. The problem with that is while the math and geometries check out there's no practical theory on creating one.

I'm talking about the consequences of relatively. It's not quite as simple as saying there's a strict limit on velocity. As time and space are inexorably linked.

Not only can we observe objects traveling faster than the speed of light. As we see with the jets from pulsars pointed at us, but this in no way breaks relativity despite people being confused when they initially learn about this.

In addition you can indeed keep accelerating forever if you've got enough fuel. People see the speed of light as this hard "speed limit" you'll hit and be unable to surpass. But in reality the speed of light is always going to be C relative to you. That means that, if you accelerate to say 50% the speed of light. You won't measure the speed of light as 150,000,000 m per second. You'll still measure it as 300,000,000 m per second relative to you. And no matter how fast you accelerate you'll continue to measure it as C in your reference frame. You can by consequence continue to accelerate forever. You'll never hit the speed of light because it's always going to be 300,000,000 meters per second faster than you. You will be a consequence of time dilation and spacial contraction travel distances you initially considered to be substantial in increasingly short periods of time, and distance, towards infinity. There is no "strict limit on velocity" in this manner, that only applies locally.

If you consider a spaceship that accelerates away from earth at a constant acceleration of 1g towards the Andromeda Galaxy. The people on that spaceship will arrive in the Andromeda Galaxy, a distance of 2 and a half million light years. In about a decade or so. The observers from earth will see the ship accelerate to but not quite reach half the speed of light, and arrive in Andromeda about 5 million years in the future from their pov.

But should a ship from the Andromeda Galaxy leave at 1g acceleration towards the earth, we would see the journey taking approximately 10 years. And we would measure the speed of it as a huge multiple of light speed. And this wouldn't break relativity at all, as the information from the ship, the light emitted from it, is arriving to us long after the ship has "left" the result is of course we see the ship and measure a velocity that exceeds C.

It's quite simple that from any reference frame the maximum apparent speed of any approaching object is infinity because light appears to us to instantly appear from its source. The maximum apparent speed of any object moving away from us is half the speed of light because for an object traveling away from us at C it takes the light from that object an equal amount of time to get back as it took to get there in the first place.