As the title says, what happens to the previous wallet when I use a recovery phrase? For instance, if my wallet has an address "xyz" and I use a recovery phrase on the other computer to recover my funds, what happens if I send funds to that "xyz" address? Will funds be displayed on both computers? If not, what happens to the wallet that's on the first computer? Will the address for a new wallet be different from the old one?
When you use a recovery phrase on another computer you are providing the seed phrase for your original wallet address. This will create a list of addresses on your new wallet (including your old address). The funds will still be available in you 'xyz' address and you will be able to send transactions from it. Because your old computer also has the seed phrase to your 'xyz' address, you will be able to view and manage your wallet from your first PC as well.
All of this data, including your account balance, is stored online in the blockchain. The recovery phrase simply gives your PC wallet the ability to manage that address and sign transactions for it. Your PC does not store your coins/tokens. Hope this answers your question.