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While we perform the repair of pressure equipment, where exactly the role of PCC-2 comes in?
Take the case of a pressure vessel internal weld repair applied to a localized corrosion, how and where exactly PCC-2 should be applied?
And how does it need to interact with API 510, pressure vessel inspection code.

Primarily, inspection and repair code governs all the repair technical and management works which in case of pressure vessels, API 510 handles.
Point where PCC-2 comes in is where the kind of repair is required to be chosen for the flaw identified. Equally important in helping as PCCs are the post construction codes however, requirements listed in API 510 are to be fulfilled in full without anything missing out. From PCC-2, use whatever is needed.

So the repair type can be picked up from PCC-2 however the requirements listed in inspection code API 510 /570 are required to be applied as mandatory?
Are there not listed additional requirements in PCC-2 to be applied such as NDT requirements etc.?

See the basic thing which PCC mentions in the foreword itself is:

None of these documents* are codes. They provide recognized and generally accepted good practices that may be used in
conjunction with Post-Construction Codes, such as API 510, API 570, and NB-23, and with jurisdictional requirements.

*PCC-1/2/3.

We should not in any case go beyond this understanding of any PCC that they contain recognized & generally accepted good practices.
In no way, the recommendations should be compared to one mentioned in codes including API 510 for PVs, API 570 for piping, and NB-23 in general.