PROCESS Macro is not a full Structural Equation Modeling (SEM) program. It is a regression-based tool (for SPSS or SAS) primarily used for mediation, moderation, and conditional process analysis, developed by Andrew F. Hayes. While some models tested in PROCESS can conceptually resemble parts of SEM (e.g., path analysis with observed variables), it does not handle latent variables or complex model estimation like dedicated SEM software (e.g., AMOS, Mplus, LISREL).

thank you you so much for this clarification!!!

so my statistical test OLS regression then?

Does this mean I have to test different statistical assumptions for my correlational design compared to the ones of SEM?

PROCESS (Hayes) is primarily for mediation, moderation, and moderated-mediation using regression-based path models; standard PROCESS routines implement path/indirect-effect estimation but are not a full structural equation modeling (SEM) framework (no latent variables or full measurement models), so if you’re estimating only observed-variable mediation/moderation, PROCESS is fine, but for latent-variable SEM you should use Mplus, lavaan, or similar.

If your PhD advisor told you to use PROCESS macro it means that you have a CB-SEM model. You can perform the analysis the extension of AMOS, or you can choose another software. The new version of SmartPLS 4 allows to perform PLS-SEM and CB-SEM analysis, and has incorporated the PROCESS function for mediation and moderation. You can always use latent variables scores as measurement of the variables in the mediation analysis performed in PROCESS. This is very easy to do in SmartPLS because it allows you generate a data file with these scores after performing the SEM analysis.