There has no appeal process announced. You will be viewed as a refugee claimant not as someone on a work permit not that it necessarily makes a huge difference. Given that your asylum claim hasn’t been granted there very little chance of your spouse being approved for a TRV. The government will take the view that a family who is reunited they will be more difficult to deport if denied asylum.
You can certainly apply again if you wish. Unfortunately the chances of approval are extremely low since you are a refugee claimant.
If your asylum case gets approved and you become a protected person you can apply for a refugee travel document (RTD) and travel to a 3rd country (not your home country) to visit with your spouse. You will need to check whether a country allows people to enter with an RTD and whether a visa is required.
