Being supportive does not always mean to say, "Yes, take the job, I love you. I am so happy for you and support you with my whole heart. Go with my blessing and grab while the grabbing's good."
That is actually very superficial and lacks the depth of real understanding and support. In a comment you say to make the answer general, not just for you. So if I were the person who got this great job offer but first wanted your input before I made the decision, I'd want you to bare your soul about how you really feel and what concerns you have regarding it. I'd want you to talk to me at a time when there's nothing else on the agenda and tell me exactly what you said in your last paragraph:
On the one hand, I'm genuinely happy for you that you got this offer
because I know how much it means. I want to try to make our
relationship work no matter what your decision. [That is what I
understand you to be mean by "I want to try to make things work..."]
On the other hand, I want to be honest that it'll definitely make
things harder (especially if I can't get a job in the new city).
That will put your deepest concerns out there. I will know what I'm working with. I will know that you are being honest and that I can trust you. Knowing I can trust you to be honest is the most important thing for me in a relationship, it feels like the vital foundation on which to build, i.e. a form of support. It will also give me permission to put my deepest concerns on the table.
Two people making a life-altering decision putting both their deepest concerns on the table can feel deeply intimate. Each can see what the other is dealing with, which aids understanding, empathy, and the willingness to compromise.
That is the best way I know to be honest and supportive. I'm not sure if you're interested in further suggestions. A compromise may be for your partner to take the job offer and for you to decide about it later. You say you are not yet living together. While you are apart geographically, you might get clarity on your relationship, and it would also give you time to find a job there while keeping the one you currently have where you are. I'm not sure if that would feel supportive to your partner or not. Everyone is different. It's just a suggestion but it's a suggestion that puts the relationship out there on the table where it belongs so long as you are not sure about it.
I understand your partner is willing for the sake of the relationship to give up a once-in-a-lifetime job offer that leads to a career life goal. If, in the end, you decide the relationship is not what you want, your partner will be short-changed. Thus, if you're not yet sure about it, your partner deserves to know. That is an important part of what honesty is about, at least for me. Maybe others are different. I wish you well.