I got curious about this and dug around a little. My hunch was that DNS was playing a role. To test, I connected to a few remote VPNs to see how this page would load up.
Here is Thailand:
Mexico:
Vietnam:
Hong Kong:
It looks like the Google Translate API is configured to default to certain languages based on the location of the DNS server the site is connected to.
Interestingly I connected to Vietnam in a regular browser window (not private), and it still loaded the language for Vietnam. That tells me whatever cookie data Google uses for Google Translate does not factor in to the behavior of this widget (I think it is just DNS).
@Dr.porkchop unfortunately for you, it looks like Google has assigned the Sinhala language to the DNS servers in Sri Lanka. Any websites that use the Google Translate API are probably going to default to that as long as you are connected to a DNS server in Sri Lanka. Practice learning what "English" and "Tamil" look like in Sinhala! 