Confusion about decibels
Short answer: $p_\textrm{dB} =\alpha\textrm{ dB}$ means multiplication factor (no unit) while $P_\textrm{dBm} =A\textrm{ dBm}$ is truly a power, nothing more!

Then $p_\textrm{dB} + P_\textrm{dBm} = 10\log_{10}(10^{\alpha/10} \times 10^{A/10})$ is a power, hence has unit $\textrm{dBm}$ in logarithm scale.

$p_\textrm{dB} + q_\textrm{dB} = 10\log_{10}(10^{\alpha/10} \times 10^{\beta/10})$ is factor, hence no unit (or $\textrm{dB}$ in logarithm scale).

$P_\textrm{dBm} + Q_\textrm{dBm} = 10\log_{10}(10^{A/10} \times 10^{B/10})$ is a power square ($\textrm{mW}^2$), unit undefined in logarithm scale.