The battery guy says "if it starts fine, the battery is fine"
You might want look for a new battery guy, that is a bad assumption.
keeping the radio on for 20 minutes without it running will kill it
That’s what we call a bad battery (assuming factory level stereo draw)
First I would look at lots of mechanical reasons to have a rough/poor Idle. But I’m going to assume you have done that or REALLY are certain on the dead battery cause.
A weak Battery, will show off problems with the charging/generation system. Check you Alternator, and its wiring. When your car is running, its not using the battery at all (other than charging it). The Battery (when good) is ~12V. Your alternator puts out 13.5 -14v all the time. (that’s how your batter charges, Higher voltage makes current flow backwards into the battery)
Lots of Sensors in your engine are voltage dependent (to an extent) if your Car’s voltage gets to 8v it will stall. But this will require both the battery and the Alternator to fail.
Another possible issue is that your bad battery is ‘’‘Charging’’’, drawing so much current to try and recover that your alternator can’t keep up. An alternator is a generator, that can only make so much power based on engine speed (Power = Volts x Amps[current]). Your stall condition is idle, when your engine is turning its slowest, which means your alternator produces the least amount of current. So a big useless draw from a battery might be your problem.
Otherwise your alternator is really a 3phase AC generator, (three power outputs) that is then sent to a Rectifier to be converted to DC (in a 95’ Buick its internal in the alternator). An AC Generator works by spinning magnet inside of some wire coils. To make it’s voltage output be 14v regardless of engine speed, the spinning magnet is replaced with an spinning electric magnet, which is fed from a “Field Coil” wire in wire harness. This varying strength magnet, auto adjusts to keep outputting 14v, no mater how much current you use, or how fast your engine is turning (within the alternator physical limits)
If one of the three power outputs in the AC generator dies, or if one the Rectifier parts related to one of those power wires (a common fault), your power is bad Your Alternator output is then not true DC and will be significantly impaired. The auto adjusting nature will bring the output of the reaming two up, to try and compensate, but its a losing battle.
The big output Wire on your alternator and the “Field Coil” wire are electrically the same (95 buick I think there both in the same connector). They are separate wires because of something called Voltage drop, which occurs on the high current output wire. If your “Field Coil” wire is damaged, or the connector is dirty (really anything that ups the resistance) This will impact the alternators view of its output. Which could lower your operating voltage.
Hope that helps