Or is it a completely separate role?
No. These are three separate roles that still contribute uniquely to a project.
Service Designers are now taking the lead, but once the service design is defined, you still need technical architecture and detailed functional analysis that designers cannot deliver.
I am just finishing a major service design blueprint - I lead the work up until signing off the blueprint/vision for the project with only light coordination with BA and Architecture, but now that actual work on the project is starting I am handing down to Architects for defining infrastructure/system landscape and to BAs for detailed functional/data analysis. I don’t have the skills/interest for either of these. It still makes sense to have these three roles separate for large, enterprise projects.
You might look into a single role for smaller projects, but those already normally don’t have an Architect and/or BA…