fix: avoid stdin buffering bug in installer prompts

Prompt() created a new bufio.NewReader(os.Stdin) on each call, which
buffered all piped input on the first call and left nothing for
subsequent prompts. This made cheat un-scriptable (e.g., piping answers
via printf). Fix by reading one byte at a time from os.Stdin directly.

Also adds an end-to-end integration test for the first-run experience
(regression test for #721, #771, #730) and bumps the Dockerfile to
Go 1.26.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Dockerfile

@@ -1,7 +1,7 @@
 # NB: this image isn't used anywhere in the build pipeline. It exists to
 # conveniently facilitate ad-hoc experimentation in a sandboxed environment
 # during development.
-FROM golang:1.15-alpine
+FROM golang:1.26-alpine
 
 RUN apk add git less make