Nuclear submarines are a poor fit for China at this time.
While China remains constrained to the First Island Chain their submarines will be confined to shallow waters.
This favors the construction of smaller conventional submarines powered with modern batteries.
AFAIK China uses a bastion strategy for its strategic submarines but it doesn't use it exclusively.
The Type 003 carrier makes no sense for a strategy strictly like that.
Until China breaks out of the First Island Chain, for example by annexing Taiwan, this situation won't change.
The fact is the Chinese have more strategic depth in their own terrain than in the confines of the coastal area behind the First Island Chain.
This favors the construction of land-based mobile ICBM brigades rather than strategic submarines.
I think they need a minimum amount of SSBNs and to focus more on Attack submarines to escort the task forces of the carrier groups once those become available.
That isn't accurate.
At any time, the US has 3 nuclear submarine on patrol from Pacific Fleet and another 3 from Atlantic Fleet.
But if China commissions a fleet of 30 nuclear submarines, then China could have 3 on patrol at any time AND be able to surge 20 submarines within a few days. The majority of these submarines would be past the 1st Island Chain before opposing nuclear submarines could reach the Western Pacific. Nothing else is able to follow those Chinese nuclear submarines into the Deep Pacific.
So you would end up with a situation where many Chinese nuclear submarines have disappeared and could be anywhere in the world.
Then there are lots of soft targets and maritime chokepoints, in addition to naval ships.