I made the mistake of buying Ethereum on Robinhood and I don’t know what to do

I'm new to crypto and I bought some Ethereum on Robinhood earlier this year and made a few thousand dollars of unrealized gain. But now I realized that it might be better if I held the Ethereum in my own wallet or have it held in Coinbase.

Should I still keep the coins in Robinhood. I don't want to sell the coins and I really don't want to incur any more tax liabilities for now. I don't really plan to do anything with the coins and I'm holding them as an investment. I also read that I don't have to do anything with my coins when Ethereum 2.0 comes out and I just want to confirm that is true.

edit: or should I wait until Robhinhood support withdrawing crypto from their platform