No, it's not. It's because Americans are massive consumers. We buy things, domestically and internationally, with U.S. dollars which in turn fuels demand for U.S. dollar-denominated assets. Attributing the dollar's hegemony to its use in commodities pricing reverses cause and effect.
This is correct. But petroleum trading in dollars is an effect of the dollar's hegemony, not a cause.
Every dollar transaction contributes to the dollar's network effects. But petroleum's contribution is small and overstated. Petrodollar hypotheses are closer to conspiracy theories than useful models.
The U.S. dollar is underwritten, ultimately, by American consumption. About 15% of American imports are petroleum [1][2], so it's a significant factor. But it's not special in any particular regard.
[1] https://traderiskguaranty.com/trgpeak/what-are-the-top-10-u-...
[2] https://wits.worldbank.org/CountrySnapshot/en/USA/textview
The U.S. dollar was put at the centre of the Bretton Woods system in 1944 [1] because the United States, at the end of WWII, (a) held a global nuclear monopoly and (b) was the sole industrial power not bombed to the turn of the century. The dollar thus took its central place in global trade. That, in turn, led to oil being priced and traded in dollars.
Japan's debt being overwhelmingly domestic, priced in yen, is also not due to the petroyen (which doesn't exist).