I'm not sure what "in my experience" adds to this, but the authority conferred by a power of attorney ("POA") terminates upon the death of the principal.  Thus, your grandmother does not "ha[ve] power of attorney" relating to your deceased uncle, so your question makes no sense.

If you want to handle the administration of your uncle's estate, you will need to apply to the court in the county where he lived at the time of his death and seek to be appointed as personal representative of his estate.  Of course, that assumes his estate is large enough to require probate.  If it's not large enough, then it may be administered without probate pursuant to Division 8 of the California Probate Code.

No, it's not "still a 'probate.'"  The only probate is "formal."  Administration might be formal (i.e., probate) or not (i.e., administration pursuant to Division 8 of the Probate Code).