>I understand "lead-free" fumes are actually worse, but you should avoid all fumes regardless.
Read the SDS for any rosin available leaded and lead free. Lead free will have P260, leaded will have P261, a significantly higher risk. And P302 vs P301, and other additional risks.
Similar to lead paint, lead exposure is from lead dust primarily. Soldering produces lead dust, and it is relatively difficult to prevent further contamination
Lead free rosin is less dangerous than leaded rosin, check the SDS data sheets