Is the wood really rotten? Sure, some towards the back of the sink looks like it is pretty rough. Could you not just remove any rotten timber and use epoxy resins such as Oxera
Rebuild Resin - 1 Hour Cartridge | Oxera
Product details summary 400ml system Cure time 50min - 60min (rapid cure) Flexible, tough, accurate mixing Small repairs Sill replacement repair for damaged wood SpecificationsCure time at 20°C: 50 - 60 minutesRecommended application temperature: 0 - 25°CReady to sand and paint: 1...www.oxerarepair.co.uk
I am not a kitchen fitter, but your sink looks like it should have been under, rather than surface mount.
There are some very rotten bits, especially around the sink. I've considered filling, but it's going to look really terrible, I'd like to get rid of the black stuff.
Interesting about the sink. You're probably right, most inset ones have a wider brim to allow for sealing.