The impurities in the water causes corrosion and provides circuit paths for the electricity which were not in the phone's operating design and could damage the components. The corrosion starts immediately and is ongoing until it is completely cleaned away.
Rice does not solve the problems caused by corrosion Rice is for dinner, not repair
Try the following but since the screen is cracked I’m thinking that not only will the phone have to be checked and cleaned, the screen will need to be replaced as well.
First do not try to charge or to turn on your phone and then remove the battery as soon as possible from the phone to minimize any further damage.
Then you need to dis-assemble the rest of the phone and clean all the affected parts using Isopropyl Alcohol 99%+ (available at electronics parts stores) to remove all traces of corrosion and water. If possible do not use "rubbing alcohol" as in some cases this is only 70% IPA or less, can contain additives and is not as effective. If you do have to use it check the label to verify the amount of IPA. The higher the percentage of IPA the better
Here is a link that describes the process. Electronics Water Damage
As always with electronics, especially surface mounted pcb be gentle when handling and especially when brushing away the corrosion. You do not want to remove any components from the board. Remove the shields that may be covering some components as the water may have got in under there. The ends of any flex cables and their connectors need to be cleaned as well
Here is the Ifixit Google Pixel 3a Repair guide that may help. Ifixit sells the fix kit for the screen or just the screen itself. Click on the parts list in the screen replacement guide.
Hopefully after you have done all this the phone might possibly work correctly again.
If this process seems too daunting, take your phone to a reputable, professional phone repair service, experienced in liquid damage repair and ask for a quote for a repair. If you decide to do this, do it sooner than later.