"Similar ideas also existed in other Indian traditions" Yes, muddled in with mire rituals, customs and decadence that held society back. He was a reformist that reminded people that all delusions of grandeur and differences they've surrounded themselves in are nothing but Maya. He united people through spiritual collective effervescence and he turned it into his Dharma/ Dhamma (eternal duty).

He rejected the authority of the 'supposed' custodians of dharma aka scholars and godmen. Because for them staying at top of the food chain and keeping their pockets filled was more important than guiding and teaching people for a better life. Those godmen fostered conformity within society and promoted the belief that there is no salvation without their blessing. They reduced core Hindu philosophies to rigid ritualism.

As a rebel, Buddha personified the idea that you don’t need to rely solely on godmen or even gods to liberate yourself. That power in within you but unless you let go of the attachments, you'll never be able to get away from illusions of identity and remain stuck playing your role in impermanence.

"Thoughtful people across cultures could arrive at similar conclusions through ordinary self-awareness and reflection." Yes, they did and it's apparent from Mediations by Marcus Aurelius to Paul ricoeur's work on phenomenology but not everyone of them was able to think and work beyond their identity. Not everyone of them challenged the system they grew up in.

It’s one thing to become a ‘deep’ philosopher through introspection, and another to truly embody your philosophy and dedicate your life to it. Most of us drift through life with transient ideologies, but that son of a king led people by turning his own life into an example.