Casting, buying bait and trading fish are small actions on NEAR. Let the game sign them itself, with a key kept in this browser.
That key can only do the game's own actions on the game's contract. It can never send NEAR: topping up and buying tickets still ask your wallet.
The approval names a limit of 0.25 NEAR. That is the most the key may ever spend on fees, a little with every action (about 0.0003 NEAR). Nothing is taken now, and your account does not have to hold that much.
Every cast and every trade is written on NEAR, and each costs a tiny fee (about 0.0003 NEAR) that your own account pays. Yours holds 0 NEAR and needs at least 0.02 to play.
On the test network NEAR is free. Three steps:
Send a little NEAR to your account from a wallet or an exchange:
Copy your account's name:
Open the NEAR faucet, paste the name there and ask for NEAR.
In your wallet or exchange, send NEAR to that name.
Come back here. The game sees your NEAR by itself, and your 5 free bait are handed over.