A service provider has her Rates as well as "Extras", such as +$650 for Greek. What is the etiquette for adding the extra? I don't wish to bring it up in emails before we meet since that's frowned upon, I believe. Our exchanges our respectful and generic. Should I add it to the envelope handed over upon meeting? Or ask her during our time together...? What's the best practice?

$650 seems like a big ask for that extra. That might mean that needs time (and time is money) and a day to prepare. SOME might fast for several hours (8 to 18 hours) before the meeting. They want to make sure that their last meal has completed its passage through the old Alimentary Canal. And they might add an enema or other cleansing, too.  
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OTHERS might not make such preparations and can agree to an upgrade on the spot, in the moment. Good luck with that!  
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Based on the large extra amount, I hope she wants it to spend time prepping starting the day before so she will need notice ahead of time.  
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You could go to your session without discussing the extra in advance and see what happens. Don't be surprised if she says no, and that she needs notice. At least you know each other now so you can "safely" bring it up when setting up the next session ... as long as it doesn't conflict with other events (wedding party or other important big dinner the day before you want to see her).

but for such a large amount as this, some communication needs to occur.  

 
I would phrase it subtly such as :

I am interested in the extra you mention on your site.  

And see what she comes back with.  

I sure hope it is worth it. That is, by very far, the highest up charge for Greek I have yet seen.

Actually might be the last provider I would see for Greek. Not the huge upcharge itself but to me is saying “ I do not like or enjoy but if make it worth my while is on the menu”
Want an enthusiastic participant.

I offer extra for PSE, which to me means Greek, so yes we need time to prepare. I am not able to be ready for back door play without preparing it takes time. You need to establish the extras at the time of booking please do not wait until you’re together it’s not gonna work.