Question: what happens to ETH that isn’t staked after ETH2 is fully operational?

I'm aware that ETH can be staked for the coming ETH2 to secure the network, however, once it launches, what happens to all of the ETH that is not staked? Will it all be automatically converted to ETH2? Will it be like the split that happened with ETC and ETH where they operate independently with price and function? Or will they both exist at the same price, but with ETH2 just on a separate chain?

I'd like to understand if ETH needs to be staked in order to enjoy the benefits of ETH2, including the latest tech and probably the inevitable bull run, and what happens if I do nothing but hodl my ETH.

Sorry if these questions are basic, but I'd appreciate some genuinely helpful responses. Warm wishes to all.