Postdoc in good environment, but haven't accomplished anything on my own: How long is it reasonable to stick around? I'm about 5 months into my postdoc now, and I am seriously questioning the choice. Most posts I read about this mention bad advisors, situations with the lab, etc. but in my case actually everything about the lab is great. I'm at the top institution in my field, with an advisor that is well respected in the field and has been around for a long time. The advisor is also an extremely nice person, supportive and consistently provides positive feedback when you present work. The group is also great, full of really smart, but really friendly people. They work a lot, but that's really the only flaw in the group culture (aside from not being the safest in lab maybe). The group is also well funded, and my advisor is supportive of working on anything that is interesting. It seems like this should be an amazing opportunity. Resources galore, support, and scientific freedom.

But here's the thing, I'm totally miserable and haven't accomplished anything tangible that I can call my own. I have helped some people with their projects, but I haven't been able to figure out something to work on that is my own. My PhD used some of the same fundamentals, but this was a relatively big switch moving into the postdoc. I expected some time would be necessary to learn new things and get going, but I barely feel like I've moved forward. I tried several ideas, but nothing panned out. Now my advisor has suggested a new project to make this device, it would be slightly more related to my PhD and we have some of the resources needed to do it, and wrote a proposal to get more, but I'm still really struggling to get going. I feel like this new project doesn't involve many fundamentals, and is just engineering together existing pieces that have all been done before. If it works it might be interesting, but I really struggle to see how I could use it to do fundamental science, which is what you need to apply to academic jobs in the field. I just feel like I am failing at a key part of being an academic, which is coming up with new ideas. At some point that has to catch up to me and my advisor will notice.

So what I am struggling with is whether I should stick it out and grind away on this new project that I don't have much faith in, find a new postdoc and try to move labs (I am not willing to move cities since my partner is also here doing a postdoc), or should I just start looking for an industry job in the area (which would almost definitely come with a much worse commute, but twice the salary)? But if I did the industry search I'm not sure how I could do that without telling my advisor because I would only leave if I got a decent offer. The other labs that would be relevant for my experience are a lot less well known, and I don't think any of them would have as nice of an advisor.
Welcome to the club of being a miserable postdoc!

I was and am in quite a similar situation.  I had the benefit of my first postdoc being with a horrible boss and lab, and my second being with an amazing boss and lab, so it has been easy to figure out which aspects of postdocing are me sucking and which aspects are the environment sucking.  During the second postdoc with the good people, it became clear that the persistent lack of passion was on me.  Even after I finally saw a few projects to completion, the emptiness remained.  I think if you're feeling consistently unhappy, it's a good sign that the academic research life isn't for you.  There are tons of other career paths where you can engage in the activities you do find fulling (mentoring, teaching, counseling, etc.) that don't require slogging through miserable research hours.

It also sounds a bit like you have a touch of imposter syndrome.  Read this for some tips on how to work through it.

I'd hold on to the postdoc at least a few months longer while you start investigating new options and figuring out finances in case you need to go jobless or re-train for a bit.  Once you've figured out a plan, just be honest with your supervisor-- it's unlikely to be the first time they have had a postdoc jump ship.