Ugh...this is the second issue relating to a recent update that broke the context functionality. This issue is best demonstrated with written instructions inside the context box -- I like to use this one:
Translate the etymological root of each toponym; localize and adapt all of them into naturalized, native place names.
Write these instructions (or anything else resembling such) to the context box in Translation Settings. Provide a term to translate; in my case, a place name; then make sure Alternative translations are shown on the right side.
The context will not apply to the alternative names, and listed names should be similar to as if you never provided context at all.
Previously, context would also apply to the alternative translations. For example, with the etymological adaptation context I mentioned earlier, it would suggest different 'flavors' while localizing the city name, like 'Deepsyke', 'Deepbrook', etc.

I compared the alternative-translations request payload with a session still on the older version of Translate. This is the old translations_options field:
{
"formality":"default",
"speaker_gender":"unknown",
"addressee_gender":"unknown",
"style":"natural",
"language_complexity":"standard",
"context":"Translate the etymological root of each toponym; localize and adapt all of them into naturalized, native place names.",
"writing_style":"general",
"correction_level":"standard"
}
The new one has the context string left blank:
{
"formality":"default",
"speaker_gender":"unknown",
"addressee_gender":"unknown",
"style":"natural",
"language_complexity":"standard",
"context":"",
"preserve_formatting":false,
"writing_style":"general",
"correction_level":"standard"
}