Go to a lighting store and ask about low voltage LED tape light ( I would not use tape light) that being said the wiring is fine but LED transformers are sometimes differently metered, and likely you should replace that as well.

I would not use led strip tape, personally. its not bright enough.

I mostly use Halo 9” and 18” under cab lights all the units i do. plenty of light and color selectable.

These are line voltage and do not require transformers.

You need line voltage to a driver that is specifically rated for the tape lights. I use Hafele lights, which have much higher quality diodes. They are more than sufficiently bright. But look better with a diffuser channel if you have polished dark stone.

You’re not using the existing wiring for new LED.