Do Coinbase, Coinbase Pro, Robinhood, Gemini, GBTC count as Web Wallet?
Does that mean when you buy bitcoins on Robinhood, Coinbase, Coinbase Pro, Gemini, or even the trust GBTC, they are all Web Wallets?

You can call them exchanges or web wallets but in both cases you don't hold the private keys and just looking at numbers based on the database used by website/app until you withdraw bitcoin to an address for which you own the private key.
GBTC is completely different from others but still you don't own any bitcoin private keys and you can read more about it here: https://grayscale.co/faq/

So should we consider Robinhood, Coinbase, Coinbase Pro, Gemini, or GBTC Web Wallets and avoid using them for too long but should transfer the private keys into our own wallets?

Keep only the funds that you need for trading on exchanges or willing to risk in case exchange gets hacked, shutdown etc. Withdraw everything else to your address for which you own the private keys.