PS5 uses "highly programmable" voice-coil actuators to deliver vibration.
These little motors are the same kind of technology that allows speakers to vibrate and create sound, which means they're able to produce much more precise movements than the larger, spinning rumble motors.
What makes the PS5 controller's haptic feedback different is the nuance of its vibration motors. Inside each grip of a PS4 (and PS3) controller, there is a large motor with a half-moon-shaped weight, capable of spinning at various speeds and for various durations. These motors can help create immersion-enhancing vibration, but they're fairly crude and aren't able to start and stop very precisely. (Screenrant)
Since old PS3 games are meant to work with old Dualshock controllers, they shouldn't fully exploit the new controller's technology.
You need to sync the controller with the PS3 before it'll work with your console.
To sync your controller, connect it to the console via the USB cable, the 4 lights on the top should flash. Now press the PS (i.e. Home) button (large round button in the middle of the controller, between Start, Select & the analog sticks). Only one light should flash now. You should now be able to disconnect the controller and use it normally.
If this doesn't work, it could be your controller or console are faulty.
If you are starting up the PS3 for the first time, or in safe mode, it will need to configure its HDMI settings through your TV. Sony takes you through the steps on the startup screen. However, I think you must have a DualShock controller plugged into the USB port to advance.
The black screen may be the PS3 adjusting the screen resolution, but it may also be a loose connection, which could be an HDMI lead fault. Try using a lead you know works, wiggle it about a bit, or change the HDMI port on the TV you are using.
If you bought the PS3 from a store as "used", they have a duty to make sure what they are selling works including all peripherals.
This may or may not be useful. Just some thoughts.
Best Answer
I don't think so.
According to WIRED:
These little motors are the same kind of technology that allows speakers to vibrate and create sound, which means they're able to produce much more precise movements than the larger, spinning rumble motors.
What makes the PS5 controller's haptic feedback different is the nuance of its vibration motors. Inside each grip of a PS4 (and PS3) controller, there is a large motor with a half-moon-shaped weight, capable of spinning at various speeds and for various durations. These motors can help create immersion-enhancing vibration, but they're fairly crude and aren't able to start and stop very precisely. (Screenrant)
Since old PS3 games are meant to work with old Dualshock controllers, they shouldn't fully exploit the new controller's technology.