Usually, if you find a bright green cockroach it means it has just molted and will shortly, as the air dries its carapace, turn the expected brown. The green banana cockroach (Panchlora nivea), however, is always green as an adult, freshly molted or otherwise. (Nymphs/juveniles are brown.) The “nivea” in its name means “snowy” — it’s actually a rather attractive little insect. Adults are only about 2.5cm long.
The green banana, or green cuban, cockroach is native to the “subtropics” — Cuba and the Caribbean, and is also found, as an “adventive traveler”, along the Gulf Coast from Florida to Texas. It is rarely found indoors, and is not generally considered a pest (always a refreshing find when you’re researching cockroaches). Some people keep them as pets.
Listing for this individual on iNaturalist is here.