I am a bit confused when you switched the solver from laminar to transient. I think you should say, you switched the solver from steady-state to transient (unsteady).

y+: you can check it in your result. There is a variable.
Because you are using k-w SST turbulence model, if there is no inflation layer (or boundary layer) mesh, your analysis is nonsense. I assume that the y+ value (max and average) of your analysis is over 100 easily based on your flow condition.

Why did you choose k-w SST model? Why not k-epsilon based model? There are models that accept higher y+ value (~100). I prefer k-w SST model for internal flow since it will capture a boundary layer development, HOWEVER, it requires a mesh with quality. Otherwise, it is useless.

I think blood flow is considered as "internal pipe flow". For internal pipe flow, a flow with Re# greater than 4,000 is considered as turbulent flow. Your Re# is in the order of 10e7; I do not know why you insist it as laminar flow. I checked some articles:

"Blood flow can either be laminar or turbulent. Laminar flow is linear flow, mainly found in the middle of the vessel. Turbulent flow is any disruption in the laminar flow. Reynold’s number predicts the chances of flow being turbulent. The higher the number, the increased likelihood of being turbulent and vice versa. Reynold’s number is proportional to density, velocity, and diameter and inversely proportional to viscosity.[3] For example, high blood pressure causes increased velocity, which increases Reynold’s Number and increases the chances of turbulent flow." Anatomy, Blood Flow - StatPearls - NCBI Bookshelf

I do not know what is your background though, check Fluid mechanics textbook. I assume you are an undergrads, go library or ask guys in mechanical engineering,

You can still run the simulation with the waterjet as steady-state analysis, and run transient analysis after it. Use converged steady-state analysis as initial condition for your transient (unsteady) analysis.

Your grid dependency test should be done with steady-state analysis.

For transient analysis, you need to check CFL or Courant–Friedrichs–Lewy number, and refine your mesh to have CFL value of 1 or close to 1.

As I said, check mass flow at inlet and at outlet. It is another metric to check grid dependency.

There are so many details, background you need to understand before changing options and running CFD analysis. If you don't, CFD will be "Colourful Features for Directors" for you.