From what I heard it never was 100% percent invisible to radar, but it's return was so low if it did occasionally show up as a blip, tracking systems would read it as a bird.
Incorrect. The F-117 was trackable from day one on low band PPI radars, particularly on "antiquated" Soviet equipment. The F-117 was designed to reduce the probability of lock on from high frequency fire control radars. That was easily discernable from the original emissions and susceptibility test data and the British were tracking them from the Persian Gulf during Desert Storm using low band PPIs.
I would think that any search radar would have software to assist in the process of identification & tracking. It would seem likely that the radar software would be programmed to ignore small objects (low reflectivity) so as not to distract the human operator with birds, clouds & anomalies. IOW’s the F117 would turn the radar’s own software against it.
Allegedly the HAVE BLUE prototype was tested against a Hawk battery. The operators were very experienced & they tricked up their radar for the test & still couldn’t ‘see it’ until it went right over them. Too late. You’re dead.