Is it permissible to use the new official birth date (July 2), recorded in government records, instead of the original date (July 1), in order to calculate end-of-service benefits and retirement pension in a way that ensures benefiting from the annual increase?

If your date of birth was changed to July 2nd instead of July 1st without your request, but by the action of the civil registry administration, then there is no blame upon you for using this date and taking whatever salary increase and entitlements result from it, because you had no hand in that. Correcting the date is preferable if possible.