Importantly, fumes do not contain lead. Lead oxide fumes only start occuring above 450°C, well above normal soldering temperatures (320-370°C).

The P100 filter catches airborne particles larger than 0.3 microns. Solder fumes are partly particles down to 0.1 microns, but also gases produced from vaporization of rosin; e.g. toluene, formaldehyde, styrene. Those are molecules a lot smaller than 0.3 microns. So the answer is no, just a P100 filter does not solve everything.

If you need to use a mask, I would suggest a 3M 7500 half-mask with the organic vapor/acid gas/P100 combo filter. I use one for glue work etc. and it's got a very tight seal and is pretty comfy (relatively speaking). Will cost you about $40-$50. Does require a relatively clean shave and proper fitting (sniff test) to be effective.

Or you could get a benchtop soldering fume extractor with an activated carbon and HEPA filter, which is a lot more comfortable. Also more expensive though.

Cheapest solution is doing like a friend of mine, using his shop vacuum with HEPA filter.

Actually, the most bare-bones cheapest solution would be to solder outside with a slight breeze. Only works in certain climates and times of year, tho...

You learn something new every day, thanks!