I go to Thailand regularly, and have family there. Have been there often in the rainy season.
I'm from Seattle so Goretex is my religion, but in Thailand it's all Umbrellas. No raincoats or rain hats - it seems like opposite world to me.
Keep in mind that the rain is not all day - it's usually just hot and humid and sticky and muggy, then the sky splits open and it rains HARD for a while. Maybe just 15 minutes, sometimes for an hour or three, but then it stops, and after an all-too-brief and refreshing cool-down, it's back to incredibly hot and humid and muggy. So you certainly need to plan for serious rain, but it's not an all-day thing.
Thais will be in whatever they usually wear - lightweight clothes, often flip-fops (but also standard "western" business or fashion attire, monks in orange robes and flip-flops). When the rain starts, the umbrellas come out, people manage. Do anticipate the streets running with unbelievable amounts of water so either be very careful where you step to avoid stepping into deep water (good luck) or wear something (like flip-flops or other rubber sandals) that don't absorb water. Localized flooding is not uncommon. But it's all routine, generally no big deal, the locals will take it in stride.
I still pack a good waterproof Goretex hat (I never go anywhere without it - it also works to keep the intense sun off) and a lightweight raincoat (packs to the size of a softball). I'd only use the rain jacket if I'm caught out somewhere (at a temple or ruin or on the deck of a speedboat crossing to an island - saved my bacon). In all urban areas, the umbrellas are everywhere (don't bring one, you can always find one).
Learn this phrase: "mai pen rai". Literal translation is "it doesn't matter" but it's commonly used to express "no problem!" You will hear it a lot.
Enjoy the land of smiles.