Zalman, which posek says a jacket is necessary, with or without a tallis. In south america is is considered “respectful” in just shirtsleevs, because the hot weather does not lend itself to wearing a suit. The halacha is clear about dressing the way one would dress when meeting someone important. That is a guideline. It is different in different times and places.
When I was in yeshiva my rebbe explained this halacha in terms we would understand. You should treat approaching hashem with your bakashos the same way you would the father of a girlyou are meeting for a shidduch. You should dress the same way too. Lose the arrogance and dress bakovodik.