Anyway, you have the sed you need, so that's good!
You have cat on BusyBox, which is also good, but you don't need it here:
sed -n -e 'H;${x;s/\n/,/g;s/^,//;p;}' OUT
As you asked, the sed appends every line from the file it's reading to the "hold space" (H), and on the last line ($) swaps it with the "pattern space" (x), and then, since the entire file is effectively in the pattern space, can go about replacing all the newlines with commas (s/\n/,/g). Finally it tidies up the leading comma (s/^,//) left by H before printing the whole lot (p), that was initially prevented by the -n option.