I see two pathways the PLA-navy can evolve for the foreseeable future, between now and the next 15 years.
option 1: develop global power projection capabilities
option 2: project power up to the 3rd island chain
Option 1, would favor investing heavily into nuclear propulsion. There would be more nuclear powered warships like carriers and submarines being built. Diplomatic relations with distant foreign nations would have to be established for the creation of over seas naval bases, especially on other continents. A lot more at sea replenishment ships would need to be built.
Option 2, would favor investing in diesel power over nuclear propulsion. The 3rd island chain is at most 8,000km from mainland China. Diesel powered warships are capable of coving this distance and they are cheaper to build than nuclear therefore more can be built with the same budget. Long distant oversea military bases would be less important. Fewer at sea replenishment ships would need to be built.
Question: is there any indication as to which path the PLA-navy is choosing or are they being completely silent on this issue?
IMHO, for the near future, Option 2 would be their target simply because of their unresolved civil war. The time to reunification and how it is achieved will determine how soon they'll be in the position to transition towards Option 1. And when China finds itself in that position, it'll be nothing like what the US have right now. In other words, their power projection will be only to certain regions such as Northeastern Africa and SouthEast Asia, not Europe or South America. As of now, what they've been doing is protecting their trade routes from piracy (See their Gulf of Aden missions), evacuating citizens from trouble spots and providing humanitarian aid. Don't expect them to act unilaterally and given their efforts at the UN and this "multi-polar order," any military solution would most likely be under the UN banner or coalition.