Welcome to the Forum.  I'll be pleased to address your questions.  I also want to thank you for reading some of our earlier replies- your familiarity with the information we have provided others will allow me to go straight to your questions related to this low risk exposure:

1.  That your partner was originally from Viet Nam is not as an important risk factor for STI as the fact that she is currently a commercial sex worker.  Presuming that she has been here in North America for more than a few months her recent behaviors are a greater risk factor than her country of origin.  And, as you know from your reading, the likelihood of her having oral syphilis is tiny and really not worth worrying about (more on this below).

2.  You already know we would not endorse your "just in case" treatment but I do understand your concerns and motivation for treatment.  The treatment that you received would not only be effective as treatment for gonorrhea, chlamydia and NGU but would also treat a syphilis exposure.  Studies have shown that the ceftriaxone you received would prevent syphilis and, for many patients, so would the azithromycin as well.  thus you can be confident that, even if you had been exposed to syphilis, your infection would have been cured/prevented.

3.  As a result of your treatment, there is no further risk for any of the STIs we have been discussing.  It is safe to resume unprotected sex with your wife. 

I hope these answers are helpful to you. EWH