Hi Bah777,
I wouldn’t send gift cards. Rewarding people for unreasonable behavior sets a bad precedent. And other residents my then see you as “soft touch” and think you’ll pay up any time they complain.
What’s happened with the airconditioning installation is over, and dealt with by the installer. No-one will recall it in a month. And one day they are going to install something, and disturb you for a day, but life will go on.
Move in and enjoy the renovations. If you work long hours you probably wont see anyone much anyway.
Best wishes.