The evidence for Plato's deep Pythagorean connections is substantial. After Socrates was executed in 399 BCE, Plato traveled extensively and spent significant time in southern Italy and Sicily — the heartland of Pythagorean communities. He visited multiple times, had close relationships with Pythagorean thinkers including Archytas of Tarentum, who was simultaneously a leading mathematician, philosopher, and statesman in the Pythagorean tradition. Archytas reportedly helped rescue Plato from danger in Syracuse on one of his visits.
The Pythagorean influence shows up unmistakably in Plato's work. The Timaeus — his account of the creation of the cosmos — is essentially a Pythagorean text, describing the Demiurge constructing the world according to mathematical ratios and musical proportions. The immortality of the soul, metempsychosis, the idea that mathematics provides the highest access to reality, the understanding of philosophy as a purification practice preparing the soul for its return to the divine — all of these are Pythagorean before they are Platonic.
The Republic's famous line that God geometrizes, the mathematical curriculum of the philosopher-kings, the structure of the World Soul in the Timaeus built on Pythagorean musical ratios — these aren't superficial borrowings.
The honest scholarly position is probably that Plato synthesized Socratic ethical inquiry with Pythagorean metaphysics and cosmology into something genuinely new — but the Pythagorean substrate is deep and foundational rather than incidental.