The screw in the carburetor's air passage will probably change the mixture slightly, but by the time you tune it with the mixture adjustment screw, the chances are you'll get it about right. The proof of the pudding is in the eating, and you've said it runs very well, so there doesn't seem to be much to worry about.
I have given it a descent run today . Found a new filter to put in it and very happy with the result. Even after running for half an hour ,I give a couple of minutes and then started it straight up again . The briggs lives again! Thankyou.