Apologies for diving down that rabbit hole, but Biblical interpretation is my niche.
So, first: the Bible doesn’t say “spare not the rod.” But there are, as F&F notes, three partial verses from Proverbs that come close enough for certain people to use as prooftexts.
Second, those three partial verses from Proverbs need to be put back into context - and it’s worth noting that proverbs are inherently poetic. Nobody claims that Aesop’s fables are about literal talking animals, for example. One of the three verses from Proverbs continues on to say that a disciplined child “will not die,” and if you insist on taking that literally then I just can’t help you.
And when you put those three partial verses in the literary context, even just by finishing the individual verses, it’s clear they’re about instruction, not punishment. This is where you start to see translators inserting their own bias, because those verses will continue by saying (e.g.) “the one who loves their children is careful to discipline them,” but the word translated “discipline” is elsewhere in Proverbs translated “instruction” - e.g. “A wise son heeds his father’s instruction,” Proverbs 13:1a.
Then there’s the historical context: how was “the rod” used 3000 years ago? The author(s) of Proverbs never use the word “spank” or “switch” or anything like that. Taking these verses as meaning “hit your child with a stick” is inserting the modern context into the ancient one. Proverbs does not explain how the rod is used, but elsewhere in the Tanakh (Hebrew Bible), a rod is a shepherd’s tool, used to guide the flock - consider Psalm 23, “The Lord is my shepherd… your rod and your staff, they comfort me.” You don’t spank your sheep, that’s just silly.
So, tl;dr - no, the Bible does not “make it very clear to ‘Spare not the rod.’” That’s nothing more than someone who wants to spank their child going out and looking for justification.