How critical is the recommendation letter for the JSPS Fellowship? Kind of panicking right now.

I’m applying for the JSPS Postdoctoral Fellowship (Short-term) and my supervisor wrote a recommendation letter that feels weaker than I expected. Most of it is positive, but there’s a line saying my “research management skills are at a moderate level” and that there’s “room for improvement.”

I’m worried this might hurt my chances since the program is extremely competitive. For those who have applied or reviewed applications:
How much weight does the recommendation letter really carry compared to the research plan, CV, and host institution?

Any insight would help me calm down a bit.

by ArkanaeL