Hello,

The naphta I' using comes in PET bottles which makes me quite paranoid about possible plastic-related contaminations...

Before transferring the naphtha into glass storage bottles, could I somehow clean/wash it as to remove any plastic-related compounds?

As long as I don't find naphtha or toluene in metal or glass containers this would be the best option to insure a clean yield...

PLUR

If it comes from the manufacturer in those bottles, then it should be fine. The makers wouldn't release it in a container that would dissolve.
Perhaps it has a coating on the inside.

Do you have the ingredients (msds) available?

Yes, I checked the msds (of the naphtha, not the bottle it came in)...

The thing is, there is no need for visible damage to the bottle for it to be leaching unwanted compounds...

The presence of plasticizers in reagents is a common problem. It causes analytical troubles fairly rarely so most people do not worry about it. In fields like marine chemistry however the presence of plasticizers in even spectroscopic grade methanol is a commonly reported challenge.
If prepping something for consumption its more concerning.
NIck Sand and Bear have both voiced comments that volatile solvents used for drug preps should be freshly distilled immediately before use.