When do you move from shared hosting to a VPS?
The question is not whether a VPS is better, but whether your situation justifies one. Four signals beat theory.
You are hitting limits
Memory, processes or execution time being exceeded regularly. If shared hosting holds you back at a level you cannot adjust, that is a signal.
You need particular software
A specific version, an extra service, or a setting not available on shared. On a VPS you decide.
Your peaks are predictable and heavy
A webshop with campaigns, a booking site with rush hours. On shared you share capacity exactly when you need it most.
You have somebody to manage it
This is the point that decides it. A VPS is not maintained automatically: updates, security and monitoring become your responsibility, or that of somebody you pay for it.
If none of these apply
Faster shared hosting or caching often solves the real problem at far lower cost.