There has never been a problem with any of this. Endorsing a PIO card with the new passport number has never been necessary, and it is even less necessary now.
My wife is a PIO and has been traveling with PIO card and old+new passports for several years. This is not just anecdotal evidence; it is standard, it is old news, and all the airlines know about it. Nowadays even the old passport is not required (see below) but you might want to carry it anyway since it's not a big deal.
There are multiple ways for you to access Timatic data yourself. One way is through
Skyteam's web interface:
Passengers who have renewed their passport since obtaining OCI status are also not required to travel with their original passport...PIO cards currently in circulation are considered to have the same status as an OCI card/booklet.