I've done a bit of pruning, much mostly dead wood or what was crossing/rubbing badly other canes.
One one of the roses a David Austin (Gentle Hermione if I recall correctly) I have seen this once I have cut a cane.
What could it be? As far as I remember this cane had no previous pruning done.
Would be a good idea to remove the rose maybe? Or it is not going to spread?

Edit: This piece in the photos is cut right from above the crown area.

Was that a cane that had looked healthy ?

I cannot remember, I cut it because it was harshly crossing into the wrong direction in the crown area.
This rose has another pruned cane that has the same weird internal look as the photos above.

It also looks like there would some white stuff too around there in the first photo.

It's a sign that it was affected by canker. The rose itself may or may not survive in the crown. Sometimes it can self-heal from canker, other times not. If it's languishing or looks like it's on its way out, you might want to replace it, but if it still has vigorous canes with what looks like healthy, new growth, I would keep it a while longer to see how it does.

When I will get back to the garden I will take more photos to show where this issue is and how the rose is looking.
But if this is contagious I will probably remove the rose because there are many roses in same spot.