Slowly getting up from bed, he took a look around at his "cell."
Tensing issues here, you start with a present (getting up) then end with a past (took a look) - enforce the same tensing, I suggest making the second one present tense (takes a look).
He even shared it with someone else. Although he was still soundly asleep,
Same pronouns leads to some confusion, suggest to make the second 'he' to something very different (Although that other guy was still-)
They'd told him that, after all, he wasn't here as a punishment. And it was, while untidy at the moment, everything he could've wanted.
Two commas for short sentences is a bit jarring. Suggest to reword and remove the second comma, so it looks like this: "After all, they'd told him that he wasn't here as punishment. And while untidy at the moment, it was everything he could've wanted."
Not that he knew much about apartments, however. Especially given his living conditions prior to his encounter with the "Authority."
Now this is a better candidate for a sentence with two commas. Suggestion: "Not that he knew much about apartments, however, especially given his living conditions prior to his encounter with the "Authority".
"cell."
"Authority."
“condition.”
Fullstop within quotes is for dialogue, is weird for when the word is being highlighted in a non-dialogue format. Suggest to move the fullstop out.
All in all, it's a good short story that sort of alludes to Todd knowing the world's come to an end and is fighting off madness with extreme repetitive routine, ironically an insanity of its own.