How authentic is the story of the spider web at the cave of Thawr?

Today I've come across this story : > ... > At last, the soldiers were very close. David ran into a cave to hide. > He heard the footsteps of the men and knew that they would soon find > him. David was so afraid, his bones shook and hurt. > > But then David saw a big spider at the front of the cave. Very > quickly, it was spinning a web all the way across the opening. Just > before the soldiers came up to the cave, the spider finished the web. > As the men started to enter the cave, they ran into the web. "Look," > they said, "This web is unbroken. If David were here, he'd have torn > the web to pieces. He must be hiding somewhere else. Let's go!" It bears striking resemblance to the following story that is believed to took place during Hijrah, well known by most of the Muslims: > ... Their Prophet (peace and blessings be upon him) was accompanied by his > best friend started their journey in the depths of the night. They > managed to leave Makkah, despite being hunted down. They hid in a > cave. It was late at night and they were in danger. Alhamdulillah, > Allah is the Most Merciful. Even while in the cave, they were nearly > caught by the Quraysh…their assassins who were hot on their heels. > Then there was a spider. It spun a web to protect Prophet Muhammad and > Abu Bakr Siddique. The Quraysh people came and they saw a spider’s web > worth days and days of work. So there was no doubt that the two men > could have hidden in the cave without such a large spider web in front > of it. I wonder what scholars think of the Muslim version of the story. Do they deem it as a fabrication/part of Isra'illiyat or as authentic?