* if you don't really know what you should/could be working on but are feeling frustrated with your daily routine, you should bring this up with your manager.
* if you still don't know company vocabulary and don't feel involved in the company after a few months, there may be an onboarding / culture sharing issue at play.
That said, maybe you should play the "money game" (as in the movie about baseball). It may be impossible to find a mentor who will do it all (help you grow technically, help you find more meaningful tasks, help you feel more socially integrated) but finding several mentors who can help with each facet is probably easier. E.g. your manager should be in that list re. day-to-day tasks and company culture; an outgoing coworker for the social interaction, etc.
You mentioned that most of the team is much older than you; maybe you can create a "filial" social relationship rather than a "fraternal" one. In my experience, this works quite well if your coworkers are old enough to have kids in high school/college, and you've graduated a few years ago - easy to relate to what they're going through and reassure them that their kids will eventually turn into fine upstanding folks just like you. Plus everyone loves talking about their kids.
This leaves out the big one, the dev/tech mentor... But if you're not looking for someone you can have a normal social interaction with, you can target the grumpy beards who committed 95% of the entrenched esoteric code and ask them about it. (Or, you know, just commit something that'll break their code. That usually gets their attention ;)
Try talking to friendly coworker and saying: not sure what to work on, got any suggestions?
2. I haven't become a better software developer since I left my first job; in fact, I've done less programming since I joined a purely tech-focused company.
3. The code smells I can notice in the things I do look at I mostly have no solutions for since I don't know what a better option would be. The times I do have an idea, I play around with it and realize that the way we have the code is fine and I'm just trying to replace it with something New and Shiny (i.e., I wanted to replace the nested loops we used to search a log file with LINQ, but I realized that not only did this not really change anything, I'd have to start combing through dozens of tests that use this method to make sure everything still works which would destroy my sprint schedule).
4. I don't have an angle like I did at my last job: there was always room for a tech solution because none existed in the first place. I was able to cook up lots of small and useful things that had a direct impact on the workplace. Here, just about every problem has a solution implemented already, usually a simpler one than I had in my head. Some tools that I've seen the insides of are definitely entrenched purely because of the sheer number of code smells within; I thought this would be an angle because it would probably be much easier to update if a refactor or even a replacement was worked on, but no one can justify ANYONE'S time refactoring/remaking something that already works.
5. I'd like to learn company vocabulary; my team continues to assume that I know all of the jargon even after the past few times over the months since I've been hired where I've explained I don't. I do all the usual things like explain what I'm trying to do, why I'm doing it, and do it step by step, but it feels like the only person who seems to get me when I have an issue is my manager, and even then not always.
6. Having someone who would actually be interested in getting me involved in the company would be nice, even if it just ends up being a social thing and not necessarily a tech thing. We don't work on anything groundbreaking and we've got our list of defects like every other company, but just being able to work on something and have something to even gripe about as chit-chat would be nice.