build: switch to slog Handlers

Start using the new slog handlers. With this commit we also remove the
need for the LogWriter since we let our LogRotator implement io.Writer
and pass that in to our log file handler.

build/log_nolog.go

@@ -5,8 +5,3 @@ package build
 
 // LoggingType is a log type that writes no logs.
 const LoggingType = LogTypeNone
-
-// Write is a noop.
-func (w *LogWriter) Write(b []byte) (int, error) {
-	return len(b), nil
-}