The quantity theory of money is concerned with one currency at a time.

The trick in your paragraph above is that you introduced “$1 trillion dollar”. Of course, if you say that the sum of all transactions (in BTC) has a certain USD value, then you’ve brought the exchange rate in (through the back door).

The total value of all bitcoins could still be $10 trillion or $100 billion.

I'm curious how you think that could actually happen. If the value is $100 billion and it changes hands once per year, then that's $100 billion that changed hands, and the GDP is $100 billion. If it changed hands twice, that's a GDP of $200 billion.

Note that I'm not making a price prediction; I'm just saying that if the price is low, and the velocity isn't unrealistically high, then that necessarily means that Bitcoin is playing a minor role in the economy because it trivially implies a low aggregate value of transactions.

Conversely if the price is high, Bitcoin still might be playing a minor role, if the average velocity is very low because lots of people are holding coins for a long time. But for Bitcoin to play a major role in the economy, it would need either a high price or a high velocity, so the aggregate value of transactions is a major portion of GDP.

A really high velocity would require fast and extremely cheap conversions with fiat, so you can hold fiat and convert to/from bitcoin at transaction time.