You have the fundamental off scale or right at the reference level, so the spectrum analyzer might also be distorting and producing some of those spurious responses internally.
I'd first adjust the reference level to be 10dB higher than the signal generator output before considering the generator broken.
I recall the HP 8648B being generally well liked so I don't think it should be that dirty.
But the strongest harmonic is over 30dB down from the fundamental, so the <–30 dBc (output ≤+4 dBm) spec is being met.
Even if output power is above at or above +10dBm (SA reflevel in the picture).
dBc =
deci
Bells relative to
carrier.
So the difference compared to the fundamental emission.
And <-30dBc means they promise all harmonics will be at least 30dB weaker than the fundamental output, when output power is +4dBm or less.
The spec sheet for it can be found here if others want to take a look as well.
https://testequipment.center/Product_Documents/Agilent-8648B-Specifications-9F224.pdfEdit: Just noticed that the reflevel is at +10dBm, so the generator output is at that or above.