I notice on my flat bar bike my left hand is more prone to get some tingles and sleepiness where as my right hand is fine.

I do notice I have more pressure on my left hand, Bc there is more imprint on it after I’m done my rides.

im beginning to wonder would riding a road bike on the hoods be worth trying ?
I was thinking of renting a road bike (endurance) to see if hoods position be more comfortable than flat bar, or would this not help my concerns ?

Are you using "regular" round grips or ergon style grips? Got any riding friends that might have a bar with more sweep that you could try? You could also try moving the bar so that one side is closer to, or further away from that hand to see if it helps. Sounds like you are riding while gripping the bar too hard: " there is more imprint on it after I’m done my rides."--try loosening up your grip a little, no need to grip it so hard that it leaves an imprint.

so what I’m saying is I naturally have more weight on the left hand on the flat bar causing tingling, is it worth try riding a different handle bar? Maybe riding on the hoods would fix the issue? The grips are fine
Or is the more pressure on one hand going to be same

I had issue with Carpal Tunnel and that caused a lot of numbness when I rode my bikes. I ended up having surgery to relieve the right hands issue as it was worse that the left. For the most part the only time I had issues was when I was using power equipment when mowing he grass or riding my bike, they seemed to aggravate the nerve more than anything else. It did not matter what kind of bike I was riding either. I also got rid of my gas powered equipment and replaced them with battery powered equipment.

I don't know why there is more pressure on only one of your hands but you can try raising your handlebar, it will take some pressure off your hands. Ergon grips are also more comfortale than round grips.

Change for a thicker handlebar tape
Change for gloves with more padding at the palm or gel
Try a more flat surface handlebar to distribute pressure evenly
if symptoms get worse during night time because of your wrist position, get wrist neutral orthosis
get carpal tunnel cortisone injections or carpal tunnel décompression if problem persists