So, some days ago I put my pet Addaro to Full Steam Ahead with a Yunium Key and Lain Schematic so he could turn to a Steamwork Lain three days later. I'm a bit worried that until now this didn't happen? There's nothing appearing on that page related to the pet order I did, and I thought the three days were passed tomorrow. Now I don't know if he's going to be ready just after the 4th day or if something went wrong. Have anyone been through this wait for a little longer than they should, is that normal sometimes?
Is there anywhere I can go to see my pet's steamwork-in-progress countdown? Or if it's going to happen? Or is it just my anxiety? lol

There isn't really a way to check and see if it's done, but you should get a sidebar event when exactly 3 days have passed (from the exact time that you put in the application thing for the pet).
If you feel like it's been longer than 3 days and still nothing has happened, you could submit a ticket and ask a UA about it, they can check the logs for you and help.