Can I put playstation 2 into playstation 1 console?

While it is possible, you would need to change out the PS1 internals for PS2 internals. However, you'd still be stuck with PS2, and you'd need a custom shell to accommodate the shape, size, and screw holes. Just 3D print a PS1 style shell that fits the PS2 board. That's all I can tell you.

If you want to integrate the PS2's software into a PS1, you'd have to change many things in the software AND the physical motherboard. For example, you'd have to reprogram the BIOS, replace the GPU, add RAM, ect.… It's possible, but not worth it.