(I am not a moderator and normally the term "moderator" on the StackExchange network describes elected (diamond) mods, but I do have access to the mod tools privilege on Writing.SE and am close here on WorldBuilding, therefore I will take your sentence about "what existing moderators think is a valuable contribution" to mean "what do other people with experience on the network think is a valuable contribution". I will describe those later.)
Answers are indeed considered to be more valuable than questions on the network as a whole as you can see for example when it comes to the difference in rep gain (+5 for questions, +10 for answers), the amount of rep lost on downvotes (0 for questions, -1 for answers), the fact that you can't put a bounty on a question for the querent, only for an answer, the amount of badges that are related to answering (there are some for asking, too, but tag badges for example are exclusively for answers) and probably a few other things I forgot know. That doesn't mean people don't like questions - without questions there are no answers and a site wouldn't serve any purpose. Look at sites who struggle getting out of their Beta for example. Writing.SE is a site I am active on that aces all of their stats that are needed for graduation - except for "questions per day", which is somewhere around 5 most of the time and should at least be at 10. They would love to have more questions! Questions are incredibly important and if you want to contribute by only ever asking high-quality questions then that's perfectly fine!
In an ideal world everyone would contribute the way our elected mods do, which in general means:
- asking high-quality questions
- posting high-quality answer
- editing stuff
- keeping track of newly created tags
- guiding new users
- writing comments
- going through the queues
- keeping an eye on Meta
- voting (up and down)
- and all the other stuff our elected mods do.
But in reality we can't expect everyone to be as good as the people we elect to represent us - they are exceptional. If you want to contribute then find something on the site that you like and do that. Take a look at my answer to the Meta question Why do YOU hang out on Worldbuilding? I described how I basically never answered or asked anything on the site. I liked commenting and I liked editing - stuff that many people find boring. If you look through the comments you can see that one of our elected mods encouraged this behaviour. I later changed a bit and started answering/asking again, but I am still mainly editing (~1.2k edits) and commenting (no idea if there is any easy to find number) (and flagging (~1k helpful flags)). That's fine. That's the way I contribute to the site. Every bit helps! To cite our elected mod Michael "If editing is what floats your boat, by all means do it!" You can replace editing with basically anything else you can do according to your privileges.
I think you are misinterpreting a few things and I hope my point two has already showed that you can do a lot and that you are already doing a lot Mister "reads Meta and thinks about how best to use his privileges" - that is already something that not so many people seem to do and keeping an eye on Meta to help people who have questions about the site or to start discussions like this one is immensely helpful for the site. I can also see that you have ~150 answers, which is a lot, ~460 votes cast, which is also a way to contribute, I can see that you are reviewing stuff in the queues (yeah, taking a closer look at a profile reveals a lot of info), that you are commenting a lot - heck, you are already contributing a lot. Please continue to do that to help the site and everything is fine, no matter what your rep count says!
You can look at the privileges page to see all available privileges and by clicking on one you can get to the specific privilege that this question is about. There you have a description of what you can do and what you should think about when you can do that:
As one of our most experienced users, we're counting on you to guide the community and lead by example.
View deleted posts
Cast delete and undelete votes on questions
Access moderator tools
Edit tags inline
...which collectively allow you to help the elected community moderators in monitoring the site and helping to clean up messes.
Basically this means: you can see all the crap that people post on this site even after it's been deleted and you should make sure that it really is crap. If you find something deleted that is not crap and there is no reason to leave it deleted you should think about whether you want to start a discussion on Meta or in the chat to get it undeleted again. But read the whole page - it will give you all the insight you need.
Because basically what you are supposed to do is: whatever you are doing right now.
Yes, you can do a bit more, but it's not like people suddenly expect you to handle spam flags. There are some things only elected mods can do such as casting binding votes for closure and deletion, having queues for spam and rude/abusive posts, handling people who repeatedly do something that is unhealthy for the site... That's why you will often see on Meta sites that their job is something like being a janitor - they have to see the real crap while the normal people like us handle the normal stuff and only notify them of the really bad stuff. If you have 10k rep you will see more bad stuff and can act a bit better on the bad stuff, but the real crap is still up to the elected mods.
And everything you do still is not binding - you would need delete votes or undelete votes from multiple people to do something.
An interesting new feature you will see are the mod tools that can be accessed through a link that will appear besides the review queue. It's a small link and it's not totally easy to find, but you will find valuable information about exceptionally good and bad stuff - like exceptionally high votes or exceptional amounts of downvotes. Keeping an eye on this allows you to better keep track of which questions might be opinion-based and which answers might be crap that you should act on. It also allows you to see newly created tags, which might be a start for Meta discussions about whether the community really wants them or not.
Basically you are supposed to be able to better judge whether something needs to be acted upon and you get some tools that help you better and more easily identify these things. It's still up to your experienced judgement to say whether you need to act or leave it, which is why the tools are only unlocked at 10k rep - they are tools that assisst, not final arbiters. That's still the community.
If you are ever unsure about what to do simply open up a Meta discussion and let the community decide. That's the core principle of StackExchange and while your votes have a bit more power in some regards, you are still part of the machinery and other lower rep users can still vote to not do what you think would be right. There is some more power and some more responsibility, but nothing to be afraid of.
As a regular in the chat I think that you might have misinterpreted that statement. I am pretty sure I know what the topic was and it's just that some people constantly exhibit behaviour that some people don't like, such as asking ever-changing questions and expecting everyone to know every iteration of this...
I won't go into detail, but that statement as you have put it in your question is taken out of context and is most certainly not intended the way you seem to have interpreted it. That statement was about certain individuals, not the generic "mainly asking questions"-user on the site.
Asking high-quality questions on the site is incredibly valuable and important for the site!