Hello!
This is a classic symptom of fuel pressure loss.
When a fuel injected engine is shut down, it must retain fuel under pressure in the fuel lines and fuel rail so that there will be fuel available when the engine is restarted the next time. If the fuel pressure is slowly bleeding down over a few hours, it will result in exactly what you are describing.
Fuel pressure can bleed off through a leak anywhere in the system, a faulty fuel pressure regulator, or (most likely) back into the tank through a worn fuel pump.
To diagnose this problem, what is necessary is to take the vehicle in to whatever repair shop you normally use, and descrie the symptoms to them. They will want to keep the car overnight, and will attach a fuel presure gauge to the fuel rail before going home for the day. The next morning, they can tehn take a pressure reading when they come back in to see if fuel pressure has bled down overnight.
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