trailer bearings leak - castle nut stuck (why?)

Looks like a piece of a cotter pin still in there at the 4 o'clock position. There may be two holes.

If you would adjust the pliers correctly and engage the nut correctly, you could have much more turning torque.

Watched the video and the cotter pin was removed along with the excess grease so that's not an issue.

It appears to me (guessing) that the axle threads may have been damaged when the cotter pin hole was first drilled or installed. I would do a VERY close exam of the cotter pin hole on both sides of the axle looking for damaged axle threads. You may be able to grind down the damaged threads with a small Dremel tool or clean out the cotter pin hole with a small drill.

IMHO a large Crescent or open end wrench would work better on the castle nut instead of the channel lock pliers.

Was going to be my suggestion, look for cotter pin. Unless you’ve literally run all the grease out of the hub and water from boat launching rusted and froze it up.

Springs rusted out and blown seal or cap off?
Is it rusted up or not?

Yes carefully wipe of fall the grease around the nut and look for a cotter pin buried down in the grooves. Most likely the pin will be at the 12 o'clock or 3 o'clock position.

does it have a cotter pin in it? They can hide in excess grease