Telling my department about switching to a new PhD program - moral dilemma Background
I'm a PhD student in a science PhD program in the US. I had a fellowship covering all costs + a stipend and so far I haven't  had to TA or RA. I'd be TAing from next year though.
I have had a shift of interest towards field B. I like to work (in academia) in a different field, and although I'm still interested in my current field, it's become clear to me through many discussions with the people in both fields that I should switch to B. I applied for PhD programs in B, surprisingly I got in despite lack of background, and now I have to make a decision within a few days to either stay in my current program and forget about field B or leave my current program and start a new PhD in B in the fall.
Interest-wise, it's clear to me that I like to migrate to field B. This is far from an over-night decision, and I let my interests in the field ripen over the course of a couple of years before getting to this stage. But I'm facing a serious challenge telling my current department that I want to leave for a new program, and I'd appreciate some advice on how I should do that.
Here is why this is challenging:

I've kept them in the dark about this decision so far (I know I shouldn't have, but it's part my personality not to share important updates until they're finalized and part the situation wouldn't allow me to do that confidently). I have signaled my interest in field B, but as an interdisciplinary interest, and as such, I've been encouraged to pursue it by my department.
My current department and advisor have been extra nice and cooperative with me. They supported me so kindly through a personal hardship I went through, while they definitely didn't have to.
So far, I've been on fellowship, only takin courses, exploring, etc., and no research or teaching output. Now I'm at a stage that I'll soon start &quot;paying off&quot; for the department's investment in me, and it feels morally wrong to leave now, after taking their money and giving nothing back.
There's an important milestone in my current program that's approaching within days, and I have to tell them before they actually start working on that, because that'd make it even worse if they put all the effort to send me to the next stage and then learn that I was planning to leave soon anyways.  Of course they know I've made serious decisions about this quite a while ago that now I have an offer. I'm afraid they might feel used if they learn as they were providing extraordinary support for me, I was preparing for leaving them without telling them anything about it.

My questions:

What's the best way to approach this and tell the department about this?
The truth is I've been in a situation that personally I couldn't put my mind into making this decision until this past week. I've had some time to clear my mind now, and I want to make this transition, but the items above are holding me back. As I said, I don't dislike my current field, so I'm even wondering if what I'm doing is so unethical, perhaps I should stay. Is this so unethical?
What's the best way to approach this and tell the department about this?

There is no magic incantation; the approach will be the same as for any other job. Tell them as soon as possible, thank them for all they've done for you, and emphasize that your decision is based on your evolving interests rather than any shortcomings of the individuals involved. See also this post.

I'm even wondering if what I'm doing is so unethical, perhaps I should stay. Is this so unethical?

There is nothing unethical about it; grad programs know that a fraction of students will choose to leave due to circumstances beyond the program's control. Losing a good student after investing effort is disappointing, but it goes with the territory. You should not let such considerations hold you back from doing what you need to do.

perhaps I should stay

You didn't really ask for advice on the decision itself, but I do want to say that many students fixate too much on the exact subject they're studying. The idea of a PhD, however, is to give you a foundation from which you can continue to learn throughout your career. Now if field A is art and field B is physics, yeah, you will have to switch; no way your art foundation will be that broad. But for most adjacent fields/subfields, either PhD should give an adequate foundation for your future work.
Beyond that, staying seems to have three key advantages:

Your department is &quot;encouraging&quot; you to pursue B as an interdisciplinary subject. From the outside at least, this seems like a &quot;best of both worlds&quot; situation.
You don't have to restart you program from the beginning, which will save you an entire year
You get to stay in your current supportive environment with a great advisor. Grad programs are a bit of a dice roll; rolling again introduces some uncertainty.

So I certainly recommend that you consider staying on. But at the same time, if you're not really passionate about A, you will not be successful in A, and it's certainly better to make the jump now rather than three years from now. So it is a dilemma, and one only you can unravel; best of luck.