Historically you have NOT been able to transit through Bangkok to Phuket. Some people say that's changed, I saw a proposal a few weeks ago but haven't seen anyone actually transit through Bangkok to Phuket.
Yepp you're fine. Originally you didn't need to book a PCR test, but when they added the 5th day test you need to buy that separatly, I forgot about that. But yes, your hotel booking includes the 1st test.
Unfortunately they don't make it clear, but it was rejected because you haven't done one in person 90 day report yet. You need to go to the Bangkok immigration center and do a 90 day report. You can report 14 days before up to 7 days after your report date without a fine.