Support said the sub is active now , so that is good to hear
There is an issue on the account that caused the steam time not to apply to the account , you need to call to resolve that issue
maybe try using skype or similar to call , you still need to provide the screenshots so they can add the gametime once the account is fixed
I'm having the same issue too.
My game tag is AssassinLVL
You will need to call swtor support when the phone lines are open to fix an account issue on that swtor account
https://answers.ea.com/t5/General-Discussion-Technical/INFO-Getting-Help-and-Board-Guidlines/td-p/48...
also email per the steam purchase in https://answers.ea.com/t5/General-Discussion-Technical/INFO-Steam-Purchase-Not-Working/td-p/9356718/...
check they have your email when you call to fix the account , if not ask to upload the screenshots to a case whilst on the phone
