I think you need to find out whether the PCR test requirement applies to transit passengers or not - if not, you are all clear; if it does, then you need to comply. It is not TG making the rules, but the Indian government, yet TG has to enforce them (and rules tend to change). PCR tests should be ok from any location as long as it is taken within the timeframe mandated by the government regulations, so getting them in HCMC should be fine.

I have not checked as it does not apply to me, but do also check whether the Thai health insurance requirement for pax going to countries requiring pre-flight tests is still in force, as you will be departing Thailand on your return flight.

For contacting the airline, have you considered Skype through WiFi somewhere? - that would probably be the best option for you.

Sorry for not having many answers, but I hope the above helps in some way anyway