Are filtered solder fumes safe?
That &quot;filter&quot; doesn't really do anything.  The fan however disperses the fumes, which are then ideally vented out by the HVAC system without reaching harmful levels.  How safe that is depends on how much air exchange you have and the volume of fumes you're generating.
Edit: I'm surprised this is controversial, but those &quot;charcoal filters&quot; are  worthless at removing particulates, which are the primary component in solder fumes.  Take a look at the particle size that will fit through them:

Those millimeter-wide gaps are literally thousands of times too large to remove the sub-micron particulates generated by soldering.  Activated carbon is more helpful at removing gases, but again, the surface area is negligible and most gases will pass through without ever encountering any surface at all because the filter is simply too thin.  If you have one of these, you are depending on the HVAC system to exchange fumes for fresh air.  There is a whole EEVBlog episode going over this: https://www.youtube.com/watch?v=ffaiKZMU0Lw
This isn't just my opinion either.  Here is a quote from a study evaluating activated carbon foam filters for solder fume extraction:

Activated carbon filters in the form of foams, used with the simpler
type of cleaner, had negligible filtration efficiency against either
particulates or vapours and would, therefore, offer no protection
against any hazardous component of the fume.

Measurement of the Performance of Air Cleaners Against the Particulate Element of Rosin-based Solder Flux Fume
If you can't get access to that ventilation and are going to be generating any serious fumes, then you need a HEPA filter. Otherwise you're just blowing the same particulates in a circle and then breathing them in.
Those generic HEPA filters Dave Jones talks about in the EEVblog videos are relatively inexpensive and they're generally effective (will remove smoke and the order of burning flux from a room), can actually remove particulates, and the filters are interchangeable if you want to buy a name-brand or certified replacement filter rather then trust the generic parts.  If you can't work in a well ventilated space, they (at a minimum if not something better) are worthwhile.