It really depends on your lifestyle and where in Thailand you intend to stay. My first time in Thailand I ran through $10k+ in a month and spent most of my time in Bangkok and Phuket. I had an amazing trip, but it wasn’t necessary to spend this much. Your current budget is definitely doable but I would try and increase the $500 leftover to $1000 to be safe.
I’ve been in Japan the last 4 years using my T Mobile plan. Just make sure to set cellular data to your local line and don’t enable data switching. You should not get any warnings. I also pay $140 for 3 lines (Magenta Max plan I believe).