Thankfully its working now !!
Fix #1
You just have to zip ONLY the files and upload it on lambda function else it won't be able to find your file.
Fix #2
I did switch the regions in between which could potentially cause misunderstanding so i deleted existing functions and API gateways and made new one.
Fix #3
I replaced the Access-Control-Allow-Origin: of api gateway from "*" to my deployed URL link.
Fix #4
I increase the Lambda timeout to match or closely align with API Gateway’s 29s limit.