What is wrong with my guitar amp?
You have a number of problems that I can see.

First, your grounds. You must learn that solderless breadboards, while convenient, are very bad for audio work. Using as short a jumper as possible (like, about 1/2 inch) connect pins 3 and 6. Then use a somewhat longer jumper to connect pin 6 to ground. Better yet, use 2 in parallel. Also, tie your buffer grounds to pin 3, not to the ground strip on your breadboard.

Next, decoupling. Connect your 0.1 and 220 \$ \mu {F} \$ capacitors directly from pin 1 to pin 6. Do not use these long wires, especially for the 0.1 \$ \mu {F} \$.

Third, your input AC coupling, C1. Do not use an electrolytic for this. Get a non-polarized 1 \$ \mu {F} \$.

Fourth. With no signal in, measure between pins 2 and 3. It should be zero. If not, figure out why your input buffer is messed up.

Fifth. Be aware that this is not a single-ended amplifier. That is, it does not have one side of the speaker grounded while the other varies. BOTH  outputs will change with signal changes. In general, with zero input and a 12 volt supply, both outputs should be at 6 volts.

Sixth. Your voltage calculation is only partly correct. It calculates the RMS voltage to produce 1 watt RMS into 8 ohms. However, the actual swing must be multiplied by 1.414 to find the peak voltage, since for a sine wave of amplitude A, the RMS is \$ \frac{A}{\sqrt{2}} \$.

Finally, be aware that, since you are running 8 ohms/12 volts, your chip will run hot.