I just checked the uscis website and I see updates for both cases. I751 is stating that it was approved and for N400 it says:
Oath Ceremony Notice Was Mailed
We scheduled your oath ceremony for Receipt Number IOE12345678. We sent a notice with the date, time, and location of your oath ceremony to the address you gave us. Please follow the instructions in the notice. If you do not receive your notice by December 6, 2023, please go to www.uscis.gov/e-request to request a copy of the notice.
Does it mean that we can go to their website and check the document which they've sent to us?
If yes, I have to wait for my wife to return from work as I can't login to the site without her phone.
This is exciting! 4 Months from start to finish. I can't believe it only took this little time.