A reliable method to obtain metallic nanoparticles in general is to reduce a metallic ion in presence of a capping agent. For a example, a traditional method to obtain gold nanoparticles (AuNPs) is to reduce a gold salt in presence of dodecanothiol.
For example, here is a method to obtain Pd nanoparticles by thermal decomposition, still the precursor is a Pd complex and the method requires a capping agent. (TOP stands for trioctylphosphine)
Related to the videos you post, it is not common or recommendable to obtain single metallic nanoparticles by an oxidation process (oxidizing the wires for example), it goes against what a metallic nanoparticle is. Electrolytic processes can be used to obtain metallic nanoparticles, but still using a salt as precursos as you can see here. You have to end with the reduced form of the metal if you want pure metal nanoparticles like the ones you cite in Nature's article. The videos you show do exactly the opposite and I can assure you that what is formed there aren't nanoparticles. Also, you are talking about Pt and Pd and their oxidation is not a simple task.
You can't confirm that you have nanoparticles just by checking Tyndall's effect, it doesn't works like that. You need to determine the size and the shape of the nanoparticles directly, using TEM or by indirect relation between them with another property, like light scattering or surface plasmonic resonance.
Even if you can oxidize those wires you probably won't end up with metallic nanoparticles. Because to maintain them at nanometric scale you'll need a capping agent. In the best case you'll obtain the metallic oxide or hidroxide and it will be in the bulk form.
I strongly encourage you to check articles in any of the ncbi websites https://www.ncbi.nlm.nih.gov/, https://pubchem.ncbi.nlm.nih.gov/ and others which are free and peer reviewed.