Relative to you, the other spaceship is standing still. You are both just floating there while Earth quickly moves away from you.
If you were going 90% the speed of light relative to your launching site on Earth, then if you looked back at Earth through a telescope you’d see them all aging very quickly, but to you and your neighboring spaceship, you’d both not experience any personal change. You’d be able to see the other ship and vice versa quite normally.
In fact, if you took a flashlight and pointed it straight ahead in the direction of your travel, even though you were going 90% the speed of light relative to Earth, the beam of light would leave your flashlight at the speed of light relative to you. That’s only possible because time has slowed down for you, making light always look like it’s going light speed. You will not notice any change personally.
On Earth, people looking at you in a telescope would see you were moving and aging very slowly, and although the light of your flashlight would not appear to be going much faster than your spaceship, because your time has slowed down, you see it going out at the speed of light and people on Earth are moving slowly.
Consider this. Here you stand or sit. But the earth is spinning at about 1000 mph at the equator. We are also going around the sun at about 67,000 mph and orbiting the galactic center of the Milky Way galaxy at about 514,000 mph, and our galaxy is approaching the Andromeda Galaxy at about 250,000 mph. So you are not standing or sitting still at all! You are moving very fast right now, but when you shine a flashlight in all directions the beam leaves your flashlight at the speed of light relative to you and your sense of time.
The same happens to you and your friend in the nearby spaceship. You can look out the porthole, see him, and wave and he can see you and wave back as if both your ships were stationary in space and just floating next to each other. It’s all relative.