How could be the concentration of airborne pathogens in a specific indoor space be measured?
I have no idea how practical it would be for your intended application, but people do estimate airborne concentrations of fungi and bacteria by sampling aerosols (i.e., filtering a volume of area to extract dust etc. that can carry the target organisms) and then using quantitative PCR with primers targeted at generic fungal or bacterial DNA sequences to estimate concentrations of particular classes of organisms.

Luhung, Irvan, Yan Wu, Chun Kiat Ng, Dana Miller, Bin Cao, and Victor Wei-Chung Chang. “Protocol Improvements for Low Concentration DNA-Based Bioaerosol Sampling and Analysis.” PLoS ONE 10, no. 11 (November 30, 2015). https://doi.org/10.1371/journal.pone.0141158.