Unfortunately, manufacturers don't necessarily use the term obsolete, or be consistent about how they use it.
I looked up the policy for NXP as a sample, they define :
Status refers to product availability and is tied to Product Life Cycle (PLC) codes. Status notations found on this website include:
Not Recommended for New Designs
End of Life
No Longer Manufactured
Available = Active. NRND is "mature, approaching EOL, but still manufactured". EOL means manufacturing will end in 2 years (specific to NXP). "No longer manufactured" is self evident, but at that point there may or may not still be stock at suppliers.
So we are still going to have to do some subjective interpretation. For NXP, we could say obsolete means "no longer manufactured" plus 6 months. As I said previously, we don't need to immediately purge parts when some arbitrary period has passed, it's just the part becomes a candidate for "retirement".