Posts elsewhere on the Forum have described the typhoon-damaged roads leading north to Cebu City on the route via Argao (online, including YouTube, it is difficult to find this information but at least two posters have described their personal experience).

I searched the alternatives for those who don't want to travel by car or bus and this seems to be the situation as at 2nd April 2022 (with the proviso that things change and information can be unreliable):

FLY: Cheapest found (BUT depends on day of travel and those who need fixed dates may pay much more) Duma > Cebu Php 1464. Cebu to Duma > Php 1769. Flight 55 mins. Flights shown daily.
FERRY: 1) Oceanjet Ferry via Tagbilaran 2 hours + 2 hours (plus waiting time of ???) but cannot find anything online via the site I used originally (https://www.rome2rio.com/map/Dumaguete/Cebu-City) and their own website appears desolate. Does anyone know if they still exist?
2) Direct, 6/7 hours: Shows departure Dumaguete 11.59 pm with 6/7 a.m. arrival but many hotels will take in luggage even if no access to room at that time. Ferries to Cebu are on Tuesdays and Fridays. Cebu departure is 8 pm with arrival at Dumaguete 2/3 a.m. (not such a problem this direction of travel as most who read this live in Negros Or.). Ferries to Dumaguete are Mondays and Thursdays. Fares each way start from Php400 Economy. Not sure if stated times of dep/arr can be relied upon (based on knowing those traveling Dumaguete to Dapitan have had travel times double the stated time!). Travel days (and other information) taken from website https://www.cokaliongshipping.com/#sched (which appears a very good one and up-to-date. Some other online sources are not up-to-date and show schedules for three days per week).

As an off-topic to my own topic (!) - during my search I came across details about the new Metro Cebu Expressway and provide a map below:

Obviously topography and existing buildings make this rather a circuitous route (remind me of those games where you have to run a loop over a wire without touching) - my hope is that enough major traffic avoids Cebu City and makes sticking to the Southern Highway easier (I am basing this on still being around when they finish it! Although to be fair, YouTube videos show a lot of progress). I can see an advantage for those travelling from Toledo but cannot see any reason to divert from the Southern Highway at Naga City to use the new road to travel to Minglanilla or Talisay City. Definitely no sense to use it to enter Cebu City IF the only distributor road in to the city is the one shown in blue - I assume most travellers from Negros Or. would be mostly interested in the southern part of Cebu City and I am guessing the northern parts might become more congested anyway.

Also, there is a new 9km bridge connecting Cebu City to the town of Cordova on Mactan Island. I think I would wait a while before testing it out!