What's going to work without complications for you is using an integration harness specific to your 2023 Corolla, which lets you connect the amplifier to the original system without touching a single wire on the dashboard. Basically, that adapter intercepts the audio signals your factory stereo already has and sends them to the amp without disconnecting anything. That way your warranty stays intact because technically you're not modifying the original system, just adding an external component that works in parallel.
For the physical installation, the standard thing is to run the power cables straight from the battery (with a high-amperage fuse about 45cm from the positive terminal, that's critical), then you run the RCA signal cables underneath the floor mats and following the opposite route across the car to wherever you're going to put the amplifier. The ground has to go to some clean, solid point on the chassis, not directly to the negative battery terminal. I saw a colleague do it wrong on his car, connected everything any which way and then he had weird noise in the radio, all kinds of interference. It took him weeks to fix it.
The most important thing is that you find an installer who knows how to work with those integration harnesses for your specific model, because each year of Corolla is a little different. Check first with your Toyota dealer how strict they are about this, because some won't bother you if you just add an external amp without touching the original stereo, but others are more careful. Better to have that sorted out before you spend money on parts.