Is it possible to work on extra activities (start-up project) during PhD?
Honestly, my instinct is "no".

Both startups and PhD advance in the same way - the massive influx of effort. And that effort is often unpredictable. Both settings have "crunch time" wherein for the next few weeks, you might as well have dropped off the face of the Earth.

Balancing that is, imo, a very tall order for a human being and will probably result in one of them suffering, falling to the side and getting triaged if you try to split the middle.

That being said, there are paths you can try, particularly if you can manage to either consult for a startup in a way that has structured limits on your time, or manage to link your dissertation to the startup's work enough that your effort counts for double. But as entirely unrelated projects? Its begging to have one fall apart.