Everything works but turn signals, what is wrong

You have a bad ground on the left side. Use a jumper wire on the ground wire near the socket on the left side. If the lights start to work normally than trace the ground wire back to its body connection and repair

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

probably a fuse or wiring trouble

i think i would try a turn signal flasher first, it is behind the dash to the right of the steering column.

Hello

Sounds like you might need a new ignition switch...?

This means that the plug for the hazard switch is not pushed in all the way. The turn signals will not work when the emergency flashers are disconnected.

I'm not going to pretend that I'm the smartest guy on the block and just knew this. I actually had the center console apart on my 99 3.0CL and had to drive it with everything disconnected. The first thing I noticed was that the turn signals did not work.

has to be a fuse

it's possible you have the wrong bulb

Are you sure you replaced the bulb with the correct one?
The wrong bulb will make everything work wrong.
Found this to be the problem on a car I thought had a bad turn signal switch.

Could have a shorted wire or bad relay. The relay is usually located under dash panel

The Buick Century uses separate relays for the hazard warning and turn signal functions. The turn signal relay is located on the accelerator pedal bracket, and the 4-way flasher relay is located on the convenience center near the left kick panel. Try switching these two relays with one another to see if your turn signals work instead of your 4-ways.