Should i finish shinjuku now ?

No, there's no bonus SQ. The Babylon bonus SQ was for the pre-campaign for Solomon. You can take as much time as you want on Shinjuku.

there are few good and bad point finishing the main quest early

Good Point :-
quick SQ for next event
new farming spot
some event required you to finish a certain point of singularity
there's a sense of achievement since you finish the main story-line fast and quick.
Bragging Point

Bad point :-

You might get bored waiting for new singularity/event
you might accidentally use those SQ on wasteful event - incoming salt
You might use extra apple to finish the singularity

Pro on waiting for 1/2 AP:-

Use less AP = less apple
finishing several singularity at once = more SQ than finish 1 singularity
some of new event only required clearance of Solomon so EOR not than important

Bad point:-

You gonna depend on event shop or quest to farm material until you finish the singularity
some of your new servant might not able to fully ascend or skill up
you gonna a bit rush on time to clear those singularity during 1/2 AP event

I had the same question but came to the decision that the only good things to come beating shinjuku now are
1. Quartz for okita
2. Getting used to break bars
3. New farming places (hearts mainly)
Outside of those 3, thats it. Since I'm currently trying to refill my fangs and medal reserves, I'm waiting for 1/2 ap

I’m not sure there’ll be 1/2 AP for EoR...someone correct me if I’m wildly wrong, but very few events or CQs require you to clear EoR. Since the 1/2 AP is usually to help masters finish the story so that they can participate in the events/CQs, I’m not sure Shinjuku will ever get 1/2 AP (at least not until Part 2 drops at the end of the year).

It should only take you 3-4 days on natural AP. I haven’t used any apples and I’m on track to finish the singularity by the end of the day tomorrow.

there is no reason not to finish the story now. there is no event going on at the moment and it only takes a little bit over 2 days of natural AP to complete the singularity.