hi @YohanKh1,
Moving a site to webSDK does not automatically prepare the data for CJA as it depends how well the schema is created. web sdk is only the transport layer, so it is your xdm schema determines how well the data works in CJA.
if site c migrates to webSDK from appmeasurement sure you
will have the upgraded better library but it is still using the adobe data object AA style (evar/prop/events fields), note that:
that data object is designed for AA/target, not CJA.

mapping props/evars directly into xdm will give you an xdm schema that looks like aa, which is not ideal for long-term CJA use.
It is recommended to
create a clean, custom xdm schema with business-friendly field names for CJA.
have sites A, B and C all send data into this shared schema.
extend as and when needed.
to answer what happens to the aa source connector note that
the AA to AEP source connector works at the report suite level. this means it keeps sending AA data into AEP as long as the report suite is active, even after site C moves to web SDK.
if the goal is to use web sdk to AEP to CJA data, you’ll eventually have to disable the aa source connector once the migration is complete else it keeps flowing as it creates oob schema and dataset from the AA source connector.
you can differentiate sites
use a datasource id field (or dataset metadata) inside your unified schema so CJA can separate site A/B/C traffic.
Also as a side note if you end up using source connector and mixed web sdk by any chance then also there is a possibility to create a common data view and this year I did a skill exchange session on how to merge multiple report suite datasets in CJA using query service + the oob AA source connector. here’s the link if helpful:
https://experienceleague.adobe.com/en/docs/events/the-skill-exchange-recordings/cja/aug2025/journey-...