Grammar – Is the Sentence from ‘The Old Man and The Sea’ a Run-On Sentence?

I am reading The Old Man and the Sea.

Some time before daylight something took one of the baits that were
behind him. He heard the stick break and the line begin to rush out
over the gunwale of the skiff. In the darkness he loosened his sheath
knife and taking all the strain of the fish on his left shoulder he
leaned back and cut the line against the wood of the gunwale. Then he
cut the other line closest to him and in the dark made the loose ends
of the reserve coils fast. He worked skillfully with the one hand and
put his foot on the coils to hold them as he drew his knots tight. Now
he had six reserve coils of line. There were two from each bait he had
severed and the two from the bait the fish had taken and they were all
connected.

I interpret it as:

In the darkness he loosened his sheath knife and taking all the strain of the fish on his left shoulder, he leaned back and cut the line against the wood of the gunwale.

Chatgpt told me it is a "run-on" sentence and there are independent clauses which should split by correct punctuation. (Chatgpt told me it was correct the first time)

So I think a comma is needed in front of "he leaned back".

Need some confirmation, thanks.