Water damage is always bad. In this case, water has likely either gotten inside the screen or is creating a short somewhere else like the connector, the connector cable, or an on-board component of the logic board. The cable is part of the screen and the connector is part of the logic board. You will need to systematically troubleshoot each component to determine which is at fault. I cannot suggest buying parts until you’ve done some troubleshooting and are willing to spend the money on a part that may not fix the problem. I would suggest trying to thoroughly clean the device of all water residue and test before anything else.
If you can, follow the iFixit guide, Google Pixel 3a Screen Replacement , to open the phone as soon as possible and clean the water out completely. Unfortunately, your phone requires gentle heat applied to the outer edges of the screen in order to soften the adhesive enough to cut through it and you will need to thoroughly clean all old adhesive(or Tesa Tape) and replace with new. Use high percentage isopropyl alcohol such as 99% to clean the screen connector contacts and any residual water or corrosion. Ensure it is completely dry before testing. High percentage isopropyl should help to displace the remaining water and evaporate fairly quickly. Make sure it is completely dry, then reconnect the cables, power on and test all functionality BEFORE placing adhesive strips/tape.
Rice is typically a bad thing, unless it is your only option. It may work some of the time if lucky, but it causes mineral deposits to be left behind by the water which increase chances of a short. Not to mention the rice getting inside the device and the starch left behind. It is also a very slow process. It is recommended to immediately power down, open the device, disconnect the battery and clean thoroughly.
I know this isn’t a straightforward answer to your question but I hope it helps.