Thanks for that second picture, it makes it a bit clearer to me now.
At least it shows the mains lead.
The secondary windings have a lot of insulation on them so they probably last ok.
Both of the terminals from the secondary to the welding rod show signs of heat stress where the blue and grey wires are twisted together. ( a bit of voltage drop there)
The duty cycle of the welder welding will probably ok, so the transformer will survive for some time in the near future.
Good to put the photo's to the server, Nigel so we don't end up with empty boxes with a red x in them.