You can use pyqgis to create a function which creates a temporary vector layer of your one selected polygon, executes zonal statistics and print the results if the python console.
Adjust the input layer names in the code below and execute it in the python editor. Then select one polygon and call the function with giveStats()
in the console.
def givestats():
vectorName = 'Grid' #The name of your vector zones layer
rasterName = 'nh_68_3' #Your raster layername
vl = QgsProject.instance().mapLayersByName(vectorName)[0]
rl = QgsProject.instance().mapLayersByName(rasterName)[0]
vl_selection = vl.materialize(QgsFeatureRequest().setFilterFids(vl.selectedFeatureIds()))
zonstats = processing.run("native:zonalstatisticsfb", {'INPUT':vl_selection,
'INPUT_RASTER':rl,'RASTER_BAND':1,'COLUMN_PREFIX':'_',
'STATISTICS':[0,1,2,3,4,5,6,7,8,9,10,11],'OUTPUT':'TEMPORARY_OUTPUT'})['OUTPUT']
for f in zonstats.getFeatures():
for field in zonstats.fields():
if field.name().startswith('_'):
print(f"{field.name()}:{f[field.name()]}")
