Bike fit / correct riding position

~3 hours on the bike Tuesday night, deliberately slow/Z2, right hand trapezius/neck area was agony by the end.

Riding was on the hoods, very low power - so supporting a lot of weight on my hands.

How much core strength does a cyclist need- is there a test - can do plank for ~3 minutes or similar?

I'm really fed up with this, it's the only thing that stops me doing longer distances.

I think it could also be a postural thing.

How are you using your shoulders/neck?
Looking at this more holistically, you might want to consider the posture that you adopt for the 8+ hours a day you spend at a computer screen at work.

I know that if I've been working at a laptop at work, and then knock out a long ride, the my back will be fucked. If I've worked at a well set up desk, I can do the same distance on the same bike and be fine.

Also - messenger bags.