I've been trying to find a certain "golden age" short sci-fi story
"Avoidance Situation" by James V. McConnell, first published in If, February 1956. The anthology you read it in must have been Starships, edited by Asimov, Greenberg, and Waugh.
alien scoutship pilot is very matter-of-fact of "Oh yes, you've discovered us, we have all the advanced technology and war fleets, prepare to be absorbed by the galactic empire"
"The Dakn Empire has learned that whenever it discovers a new civilization, it must absorb this new culture immediately. There is no other choice. And your race must follow the pattern of the thousands we have encountered in the past. There is no choice. As of this moment, you and your people are, from our point of view, just as much a part of our Empire as our own home planets. This does not appeal to you, I know. But there is no other way."
alien scoutship has the only known form of hyperdrive in the universe, called cee-squared or c2?
Lan Sur awoke to quietness. He stretched his lean, lithe legs, slowly, returning to normal awareness as he did so. Once he was completely awake, he sat down in front of the control panel again. A single amber light beamed from the board. While he had been asleep, the scout ship had come out of its C2 drive and had slowed to a stop. They had reached their immediate destination, and since he was asleep, the computer had simply turned on the protective screens around the ship and had begun a survey of the sun system they had arrived at.
[. . .]
He noted with pride that the aliens, whoever they might be, had not at the moment reached the point of development where C2 communication was available to them, but were still limited to the raw speed of light for the transmission of messages, and hence, he felt sure, for the transmission of space ships too. This meant, he knew, that he had probably stumbled onto a race of beings still new to the reaches of space who would be helpless even in the face of his own lightly armed scout ship. However, according to patrol instructions, he activated a switch that relayed all pertinent information by means of a sealed C2 beam back to the nearest Dakn Patrol base, and put in a formal call for the presence of Patrol battleships. One way or another, they would be needed . . .
humans say "prove your firepower - destroy that outermost planet while we watch"
The alien's voice boomed back, interrupting the man. "You obviously still underestimate the technological level of the Dakn Empire." The alien paused, as if checking something. "According to my analysis of this system, the fourth and outer planet is of no value whatsoever to my people. Therefore, I accede to your request. The planet will be destroyed at once."
alien scoutship complies, and the humans respond by activating their hyperdrive - which takes the rest of the star system, including the star itself, into a different hyperspace.
The control board in front of Hawkins displayed all green signals. "Yes," he said. "I think we're finally ready. Here is our answer to the choice you gave us." His fingers pressed firmly on a single red key.
[. . .]
"I wonder what our alien friend thought when suddenly Clarion, Trellis, the two other planets, and us too, just up and disappeared and left him behind?"
(Clarion and Trellis were the names the Earthmen had given to that sun and its habitable planet.)
The different hyperdrive was an accidental discovery by the humans.
"It all added up to the fact that his race had never stumbled onto the use of subspace. I know that sounds incredible, but when I checked with one of the top physicists, I found out that we happened onto it by sheer accident—and an impossibly stupid one at that—and not through any high-level theorizing. The theory came later, after the process had been demonstrated in a laboratory."
Now they will have to grab as many star systems as they can and live in hyperspace (with Sol and Earth) to escape the galactic empire.
"Do you think they'll ever find us?" Broussard asked, changing the subject. "From the look on Lan Sur's face when he told about that other world, I suspect they'll move heaven and earth to find out where we've run to.
"Find us? The Dakn Empire? I just don't know. We've got a thousand ships equipped with the subspace drive. That's a thousand or so solar systems we can pull through into subspace before they can catch up with us—I hope. But we'll have to be careful. If one of our ships is ever caught, and they discover the drive, we're all done for. I doubt that they'll show us any mercy."