Sam2, you are wrong.
The landlord does not have the right to enter at any time. You are paying rent and it is your home.
You do have to give them an acceptable alternate time. I made it clear to my last landlord that Friday afternoon and Shabbos and naptimes for my baby were not okay. If they say they are only available Saturday, suggest a time on Motzei Shabbos after you’ve cleaned up. Nobody is working then. I have never been taken up on this, they’d rather come Sunday.
I also forbade pictures. Measuring the room is one thing. Pictures that could be shared anywhere is another. I never took pictures of an apt I was considering either. It’s rude to the people who live there.
As long as you are nice about it, it will be fine.