Is it a lack of passion or competency if I don't want to leave my current position for 6 months? I am about to defend my thesis. It has been a tough journey full of self doubt, self motivation and sheer perseverance. I am hoping that I can justify the time spent on my PhD to my defense committee. I am a changed person since I joined the programme. The last 5 years were not easy and I am simply exhausted.

I want to delay my postdoc job searching by 6 months and want to continue living in the current city of residence (where I was doing my PhD).

I just want to take time off for few months from moving on to the next phase, would like to stay in my comfort zone (aka my PhD lab), would like to get my research published, search and apply for all the available options and make the next move after careful consideration.

Will it be seen as a lack of passion or competency in my future job applications?

P.S. I will get a title of research assistant (not post doc) in my lab if I decide to stay for few months in the lab.
It would depend, perhaps, on how you characterize your "gap" to a future potential employer. If you treat it as a negative that might be easily picked up. But needing to unwind after an intense five years  is pretty normal. Wanting time to publish is a positive thing. Wanting to continue current productive relationships is also a good thing. 

So, characterize it positively and it shouldn't be an issue. The competency is judged by other things (publications, dissertation...) and the passion is something that will be seen if it is there. 

But don't apologize. There ins't any need for that.