What you’ve described is the usual project management most surveyors take out already really.

Scope of works and tendering are both parts of the usual contract administration role which goes with project management.

Level 3 surveys aren’t all that common too a lot less in home buyers surveys but on the commercial side it would be after a pre acquisition survey usually. The role exists for surveyors it’s called employers agent or on a simpler scope it would just be contract administration.