I have a stasis or "suspended animation" question?

There are two basic concepts in a sleeper vessel, hibernation and cryogenics. It isn't clear if hibernation would stop aging as coma victims continue to age but their life support needs would be reduced in hibernation. With cryogenics, the temperatures are lowered enough to stop all chemical processes, however there are radioactive trace elements such as potassium within us and there are plenty of cosmic rays in space which would damage the DNA of the sleepers. It's quite likely they would have to be revived periodically in order that the DNA repair mechanisms of the cells could repair the damage.

The slowing down of time due to the velocity's speed is called special relativity time dilation and there is no impact between suspended animation and time dilation.

We're close to inducing hibernation through various chemicals such as DADLE, N2S ( an analog of H2S ), and 5’-AMP (five-prime adenosine monophosphate). We already use DADLE to preserve organs for transplants. Research is going into hibernation as a way of keeping injured soldiers alive till they could be taken to a hospital. So it is conceivable that hibernation may be used for interplanetary travel within our own solar system.

Cryogenics does have some promise but is a long way off. The Japanese have developed a freezer called the Cells Alive System where an alternating magnetic field prevents water from forming ice crystals till it is supercooled thereby preventing the damage of freezing but currently, some of that damage occurs while thawing so an equally inventive method of thawing would be required. Also the technology only works on thin tissues such as sushi which is what it was designed for.

I would say that we should have hibernation in perhaps ten to twenty years but cryogenics is a big if as it may be easier to upload the brain into a computer and manufacture a new body from stem cells.

You have the lecture on "stasis" now let me point out that it has nothing to do with time slowing down as velocity increases, which happens whether the crew is awake or asleep and does not cause sleep - the crew can not detect that time has slowed down - only happens relative to non-traveling people.

You need to study Albert Einstein's theory on special relatively to clarify your thinking as you have two different concepts muddled together.

This is all fantasy - it has not been done - so as it is fiction you are free to impose whatever "reason" you want.