Assume in your first sentence you mean 10.8V and not 0.8V.
You said the battery came with the truck 4 years ago and that it's a wet cell (standard) type. Wouldn't be surprised that it's in need of replacement. Might also just need the electrolyte replaced.
That they measured a reduction in the capacity would be a flag to me. How did they test it, was it a handheld device or a machine? To test a battery it must be under load and from what I've seen most times they don't adequately do this. Your starter is about the best load tester, slow cranking is a great warning indicator...
Still, I would check your cables first, looking for breaks at the terminals and make sure the ground terminal is solid on your engine block. The starting circuit is actually a good test because if the starter solenoid is engaged all the complex parts, computers, interlock switches, etc are working. The high current side of the starter is wired directly to the battery with a large cable and grounded by virtue of being bolted to the engine. There is a heavy cable that returns current to the battery.
I might suspect the solenoid contacts if it was just intermittent starting, but weird behavior in other places makes me less suspect of that. I'm not even sure the Tundra starter is built the same way as my old Denso start on the 22R-E, where the solenoid plunger arcs on the hot side contact and eats away to the point it no longer makes contact.
Open circuit, unloaded voltage doesn't really tell you much about the condition until the failure is major. You can judge overall condition with it but you need to be fairly accurate, the difference between 12.1V and 12.4V is important and you need the battery temp to be the same. If you think you've seen 12.1V after a good charge and it's fairly warm (but not super hot), then that would indicate the battery is not holding a charge well. I bet if you put even a relatively decent load, like the headlights, the battery voltage would drop significantly.
"Why does the U.S. care which flag will be hoisted on a small piece of land thousands of miles away?" -- Ron Paul