Is it permissible for me to combine prayers in my hometown of Al-Rustaq, knowing that I have been residing in Muscat for a long time due to work circumstances and only rarely return there?

You are permitted to shorten the four-rak'ah prayers (qasr) and combine the common prayers (Dhuhr with Asr, and Maghrib with Isha) when you travel to your hometown, Al-Rustaq, if you have established residence in Muscat and do not intend to stay in Al-Rustaq for four days or more, provided you do not have a wife residing in Al-Rustaq. This is what the Emigrant Companions did when they returned to Mecca.