They have a very large base in Djibouti, directly across from Yemen and across town from the US/multi-national base at the airport.
It's going to be interesting to see how "China, who wants to the authority of a world power" starts to run up against "China, who has the responsibilities of a world power."
https://www.google.com/maps/place//@11.5906054,43.0625938,16...
And the PLAN has 25+ Type 052D destroyers w/ 64 VLS cells apiece [0]. And HQ-9 (reverse engineered Patriot SAMs) and ground attack capable YJ-18 cruise missiles in them.
They absolutely have the capability, if they weren't busy bullying their regional neighbors in the South China Sea, who have vastly less capable warships (if any blue water).
[0] https://en.m.wikipedia.org/wiki/Type_052D_destroyer#Armament
https://www.thedrive.com/the-war-zone/water-filled-missiles-...
The PLAN seems to be more effective and less corruption prone.
Probably why they tapped a PLAN admiral to replace the defense minister, who apparently came from the missile branch.