It looks to me that this pruning cut left too much of the branch that was cut:
Should I cut again closer to the trunk?
Should I perhaps fill the hole in the center with something?
Is there a sign of any serious illness?
UPDATE: New photos:
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The cut is fine but the tree has or will have issues. You can see that there is already interior decay in the heartwood of the tree. As stormy indicates water will enter the wound and decay will continue.
On the plus side you have created a new home for wildlife.