What area should I use fresh thermal paste?

Should I apply fresh paste in areas that already have old paste?

Indeed, the CPU and GPU are the two that are “circled” in red. Use thermal paste to repaste them. Use thermal putty or grease to repaint the remaining items.

Consider applying thermal pads to the vram. Is it going to work? or perhaps the PTM thermal pad from Honeywell. Is it secure?

For the VRAM, use thermal putty as an alternative to pads. Putties are used on some laptops in place of pads.

It should function as long as the thermal pad fits the heat sink properly and isn’t too thick.

The Thermal Pad is excellent. Actually, I used thermal paste on mine, and it works just fine, but for anything other than CPU/GPU, most folks suggest putty or pads.

Is this something that resembles my HP Omen 16?

Visit YouTube to view it. Nobody can adequately convey it in words alone. Some of them are actually thermal pads rather than thermal paste. Use caution when doing so.