If your boundary conditions are not periodic, then the field interpolation will be done with no particles across the border. It is this acting as if there are no particles on the other side

Ok. Can one do something to make this better with remove boundary conditions? This blip in density is causing an unphysical filamentation that becomes important if I run the simulation on longer durations. A x=0, I am also injecting particles starting from t=0

So the results between Probes and ParticleBinning in Smilei would differ even if I choose same number of points for grids?

Currently, OSIRIS has something similar to Probes or ParticleBinning in Smilei and I am using similar number of points as I do for Probes in Smilei.

What I would like to understand from you if this density blip at the boundary is just an artefact of the diagnostics being used? Or it is real and would be present in PIC simulation cycle manifesting into some kind of plasma dynamics (filamentation in this case)?

Hello.
The density drop on the boundary measured with Probes would be significantly mitigated with an interpolation order of one (this is maybe what happened when you ran OSIRIS ?). With an higher interpolation order (as is default in Smilei), almost half the stencil reaches cells which are outside the physical domain where the density is considered 0 hence the returned density is halved.
If you use a particle binning diagnostic with bins strictly located inside the physical domain you will not be affected by the interpolation scheme. So yes, the results will differ because you are not measuring exactly the same things.

So as you can see, the density can be different depending on how you measure it. Anyway this will never impact your simulation because the density is not used to solve Maxwell's equation. Charge density doesn't have any effect on the physics in an electromagnetic PIC simulation. It is here only for diagnostics purposes.

Thanks for the clear explanations, this helps me to understand the results! For me, physics is more important, so it is good to hear that it will not have impact on simulation.

I did use quadratic shape function in OSIRIS for a fair comparison with SMILEI, and not the default one linear.

In that case they must deposit density outside of the physical domain or use some interpolation trick on the boundary. Can't be sure.
In Smilei charge and current densities are zero outside of the physical domain and the Probe diagnostics are useful to check exactly what a particle would "see" with the chosen interpolation scheme. So, as I said, this drop in charge density has no influence but it might for some other quantities and this diagnostic is useful exactly for that.