The plant extract must change since it was used as reducing agent. If the oxidized molecule in the extract has toxic properties and somehow becomes adsorbed on the surface of the nps, you can then expect some toxicity. Since you are working with a complex extract the easiest way to determine if something as I say is true is to run a toxicity assay.
Even though if plant extract has no toxicity then also it is always recommended to test toxicity assay as it is difficult to get exact idea about the surface of nanoparticles. What is more, the toxicity depends on the nanoparticles, if nanoparticles has toxic effect then it will show effect though capping or reducing agent for eg. plant extract may have no effect. So, in my opinion always it is good to test the toxicity effect for the application of biosynthesized nanoparticles.
Surely yes, you need to test for toxicity. Drug molecules in plant matrices work either in synergy or as antagonists, as such, it's possible that "if" your Ag nanoparticles are generally toxic, other agents in the plant extract matrix inhibited the toxic potential or effect, giving an overall non-toxic effect of the extract, but on it's own, it's commendable to check and determine it's individual levels of toxicity/safety.
It totally depends upon the respective nanoparticles what you are going to prepare. For example If the nanoparticles is Cd nanoparticles then obviously its gonna give toxicity to reduce it you may need to go for surface modification with ZnS.
It is necessary to carry out the same toxicity assay carried out on the plant extract on the nanoparticles. The toxicity level of the plant extract (if it is at all) may be very insignificant or very negligible in such a way that it wasn't evident in the toxicity assay but this very minute toxicity may have been amplified due to the reduction from it bulk volume into Nanoscale