  Using the global 21-cm signal measurement by the EDGES collaboration, we
derive constraints on the fraction of the dark matter that is in the form of
primordial black holes (PBHs) with masses in the range $10^{15}$-$10^{17}\,$g.
Improving upon previous analyses, we consider the effect of the X-ray heating
of the intergalactic medium on these constraints, and also use the full shape
of the 21-cm absorption feature in our inference. In order to account for the
anomalously deep absorption amplitude, we also consider an excess radio
background motivated by LWA1 and ARCADE2 observations. Because the heating rate
induced by PBH evaporation evolves slowly, the data favour a scenario in which
PBH-induced heating is accompanied by X-ray heating. Also, for the same reason,
using the full measurement across the EDGES observation band yields much
stronger constraints on PBHs than just the redshift of absorption. We find that
21-cm observations exclude $f_{\mathrm{PBH}} \gtrsim 10^{-9.7}$ at 95% CL for
$M_{\mathrm{PBH}}=10^{15}\,$g. This limit weakens approximately as
$M_{\mathrm{PBH}}^4$ towards higher masses, thus providing the strongest
constraints on ultralight evaporating PBHs as dark matter over the entire mass
range $10^{15}$-$10^{17}\,$g. Under the assumption of a simple spherical
gravitational collapse based on the Press-Schechter formalism, we also derive
bounds on the curvature power spectrum at extremely small scales ($k\sim
10^{15}\,$Mpc$^{-1}$). This highlights the usefulness of global 21-cm
measurements, including non-detections, across wide frequency bands for probing
exotic physical processes.
