This Scribe prestige class feature does not mention the exploits
Admittedly, it is an AU, so it is not a completed class or function, but it is always better to approach the text with the following basic assumption: "if it offered this option, he would say it.
Since Living Rune makes no mention of the exploits, I would say that there was no plan to grant a feat change at each long rest.
I do not recommend it because it only mentions capacity scores, but your DM may want to allow a fun crazy option. Here's why I recommend against.
At the end of a long rest, you can choose to increase by 2 the score of your choice or 1 of your choice of 1. At the end of each subsequent rest, you can change
This choice reduces the scores you have previously raised and improves different scores. (If you chose to increase two abilities, you can choose to change only one of these choices.)
Feats are an optional rule in the PHB. (p.165) You are already in the SM's discretionary territory as it is.
Achievements are a cost of opportunity; you can only select one when an UPS option is present, and then it is locked.
With this proposed feature, you could have access to every feat of the book, with a long rest in between. This is not quite balanced with all the other characters needing to make a choice and stick to that.
Day 1, you have the exploit of alert. You can not be surprised. You then have an idea of where you will explore the second day, so
Day 2, you take the initiate magic exploit, warlock, choose blast eldritch, hex and mage's hand. You then have an idea of where you will explore the third day, so
Day 3: You take the master of arms and master the techniques of long bow, long sword, rapier and sword. You will then have an idea of where you will explore Day 4, so
Day 4, you take the lucky feat. You then have an idea of where you will explore the 5th day, then
Day 5, you take Dungeon Delver …
No one else has that kind of versatility.
Crazy fun option
Do what you propose, play on a few levels, then add here an answer explaining why it was a good idea and why. Work with your DM on this. UA is a game test, so why not test it and write a test result as an answer? 🙂