"bailing out a bunch of bankers like the United States did a decade ago will not sit well with the Chinese population" Banks in China are largely state-owned, hence they will not fail either way, or let's say the CCP will do anything to not let banks fail. I doubt that the Chinese population would be unhappy about that. Banks in China are probably not at risk, but the property sector may be.

"This all started because they wanted to tap the brakes on the overheated housing market." Evergrande has been in trouble for quite a while. The new rules this year have only added to the pressure.

"We know there are a lot of Chinese banks involved." Some 170, plus some 120 other financial institutions. So, the risk is spread wide & far.

"However, what about those who are outside the country?" Who cares about foreigners?

Anyway, via CNBC: "Here are the top funds with the highest exposure to Evergrande bonds, according to Morningstar.

Fidelity Asian High-Yield Fund 
UBS (Lux) BS Asian High Yield (USD) 
HSBC Global Investment Funds - Asia High Yield Bond XC 
Pimco GIS Asia High Yield Bond Fund 
Blackrock BGF Asian High Yield Bond Fund 
Allianz Dynamic Asian High Yield Bond" 

I suppose, they can bear a few billion in losses. Their own fault for investing in China.