How can I prevent the light leaks on the side of blackout motorized blinds
Your problem is that light bounces.  White looking surfaces reflect a broad spectrum of light, and even black looking surfaces can reflect substantial amounts if smooth/shiny.   You can see from the lighting on the frame in your picture that some of the light hitting the inside of the frame is actually reflection off the blackout curtains.  To prevent the light from getting through, pretty much your only options are to block it or absorb it the best you can.
You could paint your window in vantablack, the blackest pigment humanity has come up with.  This would stop almost all of the bouncing light and give you a very odd looking, possibly overheating windowframe.  It's kind of elegant, but probably not the best solution.  A more realistic solution would be to come up with a temporary addition for the curtains when you need it to be really black.
Thick black felt is probably a good option that will give you flexibility and easy mounting without permanent surface damage.  The porosity combined with the dark color of the material help it absorb light without reflecting much.
If you want to try semipermanent so the blinds still open, I'd try putting a 4-6&quot; wide piece of absorbent material up the center post of the frame on the inside so it overlapped the edges of the blinds, and L shaped flaps on the inside of the frame to the left and right.
Note that complete blackout is extremely difficult to achieve because of the way your eyes adjust to darkness.  A tiny percentage of the total illumination available will seem like a fair bit of light once your eyes adjust.
If you want an absolute and elegant solution and you don't mind spending some money, you could look at something like Peka roll shutters or similar external security blinds, but obviously it won't be cheap and would look extremely odd on some external finishes.