+1

Delayed upshifting is a clear indicator of sticky cables. The RD spring isn't strong enough to shift against the housing friction, so it can take riding over a few bumps to finally get the RD to move. Odds are this has been going on for a while, getting worse over time. You've probably tried to compensate with trim adjustments so the shifting is now all over the board.

One quick way to confirm a sticky housing is to downshift, then upshift one gear. If the Shift doesn't happen crisply pluck the bare wire away from the downtube like a guitar string. If that completes the shift, then you know it's a cable/housing issue.

Spraying WD-40 isn't going to do it, take it apart flush the housing, spin it dry (outdoors) then grease the wire with a light grease and reassemble. However given the age of your system, I suspect that the only remedy will come with new cables and housings.