The conditions of carriage 9.2.2 are worth reading.
https://www.omanair.com/en_gb/conditions-carriage
9.2.2. Except as otherwise provided by the Convention or applicable law, if we cancel a flight, fail to operate a flight reasonably according to the schedule, are unable to provide previously confirmed space, fail to stop at your destination or Stopover destination, or cause you to miss a connecting flight on which you hold a confirmed reservation and adequate time existed to make the connection after the scheduled time of arrival of your flight, we shall, at your option, either:
(a) carry you at the earliest opportunity on another of our scheduled services on which space is available without additional charge and, where necessary, extend the validity of your Ticket; or
(b) within a reasonable period of time re-route you to the destination shown on your Ticket by our own services or those of another Carrier, or by other means and class of transportation without additional charge; or
(c) make a refund in accordance with the provisions of Article 10.2.
So it's a standard rebooking process. If you're ok with shifting to an Oman flight on a different day then they should accommodate that (and shift the return date if that means your trip becomes longer/shorter).
Or if your travel plans are time critical then you have the option to ask to be reputed on another carrier and QR or possibly MH are the main options.
The first agent you spoke to was clearly not well informed, the availability of fare buckets on your replacement flight is not a concern of yours, the airline has changed their schedule and you're subject to an involuntary change, so just be polite but insistent and tell the agent that need to sort it out and stop wasting your time.
Good luck