Just picked up a '88' Centurion Accordo that has a replacement drivetrain. It has Sora Flight Deck 8spd triple STI shifters. The rear derailleur is a Tiagra medium cage that says 9speed on the jockey wheel arm. Shifting is a little sticky. Doesn't seem to me that the Tiagra is compatible with this. I vaguely recall that 7 Spd road rear derailleurs should work on 8 Spd.

Should work fine.

Any issues with this combination of parts is likely the result of a less than smooth cable path to the rear derailer.

Often as not, the rear-most loop of cable housing, together with the cable guide at the bottom bracket, are where big improvements can be found when the cable is once again sliding against clean polymer surfaces with proper cable-specific lubricant on the cable.
There is also the common issue of one or more strands of the cable itself having broken, at which point the cable becomes less smooth and more springy as well, neither of which contributes to crisp shifting response back at the rear derailer.

Be sure also that the cable pinch bolt and washer are directing the cable through the groove in the arm that the bolt threads into (one more thing that can also greatly affect indexing accuracy).

I have a 2002 Specialized Allez triple that came new with Sora 8 speed shifters and a 9 speed Tiagra RD, with 8 speed cassette. It works fine. It also had a Sora front derailleur which broke, replaced by an Ultegra.

FWIW I also used Sora 8 speed shifters with a 7 speed cassette on another bike. It worked fine, just didn't have a gear for the last click.

The derailleur is 100% compatible with those shifters.

I would look for other issues like cable friction, worn housing, or gummed-up shifters.

The next suspect is the chain. It appears the upgrade didn't include the chain. The chain looks like the OE 6 speed. I'll check further tomorrow.

That would be very, very odd. An OE 6 speed chain might even be a bit too wide to fit through a 7-speed rear derailleur. If you replace the chain, you might need to replace the cassette.

I think I'll just put it back to a 6 speed with DT shifters