I cannot advise on laws for Oman. UK law does recognise dual nationality but that does not mean other countries do.
However, if you want to take Oman nationality and they require you to renounce British citizenship, then you must do that. You have to use specific form to renounce British nationality and pay a fee. See:
Once renounced, you cannot simply report passport lost and get another one as you would not be British anymore. However, it is generally possible to resume UK citizenship through registration once only if the reason for renouncing was that you had to give it up such as in your case.
Hope that helps. Kind regards
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