has been placed on hold as primarily opinion based. I'll have to admit the name you give something is opinion based. However, this has a name that can be cited from authoritative sources and knowing the name actually would help someone find useful resources. It has not been mentioned in the lone answer or the comments.
I would like to answer this question.
The question and my proposed answer are on topic as explicitly allowed in the help as part of: development methodologies and processes
Further, without knowing the right words it's not something easily found by doing a google search. I know it because I read about it years ago. So no, I'm not just googling for the OP.
Edit to preview answer:
Picking just one term for this and writing only about it could easily be taken an opinion based. What I would prefer to do is discuss the singular situation the OP describes. You want change. Change will break things. This needs to be described positively and accurately to all stakeholders. Not simply the users.
Users don't care about refactoring
Users don't care about transformations
Users care about working features
Your boss cares about working features
Your boss cares about transformations
Your boss doesn't care about refactoring
A refactoring is NOT a change in code behavior. If you're adding a feature, you're not refactoring.
A refactoring is changing code without changing behavior. Refactoring will not make failing tests pass. It's what you do to clean up to get ready for change.
Not everyone lives in the rigorous world of test driven development. Indeed we are not all Uncle Bob (or Martin Fowler, or Kent Beck, or...) but if you throw around the word refactoring at least use the term correctly.
A change in behavior is called a transformation in the rigorous world of test driven development. When you write a failing test the next step is to make it pass. That is a change in code behavior.
Outside the world of TDD making a behavior change in an integrated system that will require changes in multiple locations is called a breaking change. It is a transformation whether you do it rigorously or not but that term is not well known outside of TDD. At least it doesn't sound so negative.
But even if the word transformation gives you a warm fuzzy feeling this is still not something users care about. Infact, by even asking the users to think about it you're pissing them off. They don't care about your problems.
That's why when you ask for a term that fits here:
The webpage is _____ right now because I had to make it generic for all products
I'd have to agree that 'under construction' fit's nicely. What I disagree with is the very idea of users seeing the message. Even if it wasn't that term users simply do not want to be told about what they can't have. Rout them to what they can have. Don't show them tumbleweeds that remind them of what could have been.
A website should always be under construction. Heck this answer is under construction. Would an animated gif make you feel better about it?
This is why developing on the live system is a bad idea. Develop on a development system. Use a deployment plan so you can send the whole change, all at once, when it's ready.
That's why the best user friendly term for this is: nothing at all.