Setting expectations is very important in any relationship, whether it be in a personal, romantic, or work relationship. Changing those expectations is tough and needs to be done in a transparent way to everyone involved. This time, your current situation didn't live up to your expectations. That's perfectly fine. Now you need to let your supervisor know that and what new set of expectations exist.
Just sit down with your supervisor and have an open and honest discussion with them. State any mistakes you think you made in your assumptions prior to joining and that you are leaving. Give them any constructive criticism you can to help them in the future, let them know any positives you had while there, and maybe even offer to help them find a replacement for you. Basically put yourself in their role and do what you would want someone else in your role to do for you. Well, do them if you can actually and reasonably do those things.
FYI, in most situations 2.5 months isn't "very soon". In the non-academic world, that's a long time. Most people don't give more than 2 weeks notice and, in some industries like retail and food service, giving zero to 2 days notice is common.
It's unfortunate that this situation is happening, but it'll probably happen several times over your career. It's unfortunately normal and the sooner you understand and accept this, as well as how to deal with it without unnecessary guilt, then the better off you will be. There's very many different variables when joining a new job or any situation to know 100% that it'll be perfect for you. Employers know and understand this. It's why so many jobs have a probationary period (often 3-6 months), so they know you are a good fit for them.
It's actually a good thing that you've recognized the problems this early. You aren't wasting your time, energy, or mental health any longer than necessary. Being in a bad situation, or "just" an uncomfortable one, can seriously damage your self-worth, your confidence, in working other places or even wanting to work other places. I've seen people in bad work environments that are afraid to change jobs for fear the same problems will exist or be worse. They got to the point where they think that kind of problem is normal, even when everyone else tells them it isn't. They think "better the devil you know than the devil you don't know", giving up and believing every employer is "the devil".
You haven't said your situation is this bad, so that was just me making a point.
Yes, it's hard to come to the realization that a choice you made was wrong and/or that other people aren't living up to their promises, but don't dwell on it. Use it as a learning experience, deal with the emotions that come up with, and move on to the next opportunity. Unless your supervisor is unreasonable, they may take you leaving better than you think they will. A reasonable person would understand that, as a first time supervisor, they aren't as polished as other supervisors and need to learn how to do better. They should also understand the existing time and financial constraints the lab is under and realize that it's not great conditions to work under.
You have to make the decisions that work best for you, not everyone else. It's not always easy, but it gets easier the more often you do it. Don't worry about your supervisor. You leaving will likely have very little impact on their reputation and future.