It's... It's so not.
Edit: it is a great series, but it's as far from a cozy slice-of-life show as you can get without being a seinen battle series. Like, things Planetes has that definitely don't show up in cozy or SOL:
- Radiation sickness
- Cancer
- Suicide
- Asphyxiation
- Kessler Syndrome
- Multiple terrorist attacks
- Graft
- Constant smoking
- Hijackings
- Frame-ups
- Spaceships as WMDs
- Hachi's dad
Just to name a few.
Further edit: are you thinking of Space Brothers instead?