From my understanding, and the way it appears in my account, is that you essentially 'pre-pay' for a fixed amount of buying-power. You don't get any more buying-power just because you have more funds in your account. You only get what you pay for.
I'm at the lowest tier so I pay $10/month and magically get an extra $2000 of buying power. From the Robinhood help page ( https://support.robinhood.com/hc/en-us/articles/213262686-Robinhood-Gold-Buying-Power ) this buying power has all the same restrictions the SEC sets for buying on margin (makes sense). The major one being that "By law, Robinhood can only extend up to double your portfolio value in Gold Buying Power".
In practice, this means your added buying power is the lesser of the buying-power level you sign up for ($3000 in your case) or the cash value of your account. You will need to maintain at least a $3000 cash value of your account to get the full $3000 added buying-power. Robinhood mentions "up to 2x your capital". That would be the case if you had $3000 in your account. Robinhood would extend you an additional $3000 buying power. You would get "2x your capital" in leverage. However, if you had $5000 in your account, Robinhood would still only extend the additional $3000 you subscribed for, so your max leverage would be 1.6 ($5000+$3000 / $5000) .
It's different from the way most brokers work. Typical brokers will extend the max buying-power allowed by the SEC and then charge you interest only on whatever you use. Robinhood only extends a fixed amount of buying power and also, essentially, charges you interest on that amount whether you use it or not.
The BIG benefit I see, however, for Quantopian users going Gold isn't the added buying power. It's the niceties of a margin account.
No more concern about running into the SEC 'Free Ride" rule for cash accounts. (https://www.sec.gov/investor/alerts/cashaccounts.pdf) Maybe this hasn't been a problem for you and maybe one's algorithm never accounted for this, but I'll bet you have never had your account 'frozen' for 90 days either.
No more concern about waiting the T+3 days for funds to be available after a sale. This isn't really a 'problem' per se since ones algorithm probably simply checks for 'available_funds' before buying. The bigger issue is to ensure ones algorithm includes conditional code to mimic this behavior in backtests and then bypass it when running live. Without this 'T+3' code, backtests may not realistically model live trading.