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I guess those acoustic foams are to prevent the echoing of the sound inside a room and not much to prevent the outside noise. Someone correct me if I’m wrong.
Maybe you should try these (door and window seals) first and see if such noises are still present:
For preventing sound through a door you need to seal the air gaps, the sides, top and bottom. You get rubber type strips with adhesive that you can put in the gaps. There are also particular door stops which form a seal between the ground and the door and drop down when the door is closed and pull up into the housing when the door is opened. I don’t have links or company names or any details for this though. Ask around locally.
Also if your door doesn’t have enough mass then even with the above it might leak sound.
Finally it is very hard to soundproof a door, depending upon the levels and frequency your trying to contain/keep out.