And now - maybe as a partial penance for straying from the OP topic so badly here, I’ll swing back around to something at least a lot closer to the original topic …
It’s fun to listen to knowledgeable Bible readers/scholars - either from within the faith, or at least “faith-peripheral” (shall we say, ‘faith-friendly’?) wrestle with the text at the levels it is meant to be read. A recent example of that for me was to listen to Jordan Peterson and Catholic Bishop Barron talk with each other about biblical themes - among which early Genesis figures prominently. Tellingly, the age of the earth never even comes up in their discussion. Not even a mention! They’re way too busy trying to harvest all the important stuff it has to say about our human condition and about God.
But to give the OP a more direct answer: No - the Bible doesn’t say the earth is 6000 years old. But nor does it say it’s not. It just shows no interest in that question at all.