Can I consider this email from potential PI as a rejection?
It depends on what you mean by rejection. It's pretty clear that they are not willing to take you into the lab at this moment, but it's not a firm no. My read is that it's politely interested without being committal. I read it as follows:

The professor gave you specific feedback about your e-mail, suggesting they took the time to actually read what you wrote to them and consider you seriously as a candidate.

The professor says that they'd be interested in putting together a proposal with a longer deadline - this could be honesty on their part that they simply don't have the bandwidth to co-write a proposal with a short deadline.

They also suggest you contact a young faculty in their department. Depending on the department, this new faculty could be in the &quot;orbit&quot; of the bigger name, meaning that the big professor could see this as a way to keep you on the hook even though they don't have the funds to commit to you at this exact moment.

The professor didn't ask you for an interview or any follow-up. This suggests that they don't see it as even a remote possibility that they could take you on at this moment. They're then putting the ball back in your court. If you respond that you'd be interested to work on finding a fellowship with a more distant deadline, they sound like they'd be willing to move to the next step.


Whether you're in a position to wait a year (and probably two, since it will take time for your fellowship proposal to be reviewed), and whether it would be worth it for a shot to work together with this professor is something only you or those with more specific knowledge of your situation can answer. But, if you're interested in following-up, I agree with @henning that a suggestion of a phone call or video chat would be very instructive. Either you will get a good or bad vibe from them on the call, or their reaction to the suggestion (&quot;sorry, i don't have time&quot;) will help you clear things up.