There is a small pond next to my house and I observed that dragonflies spawn there. Probably so do mosquitoes, at least the location in general is plagued by mosquitoes. Standing water is a suitable breeding ground for mosquitoes, but the dragonflies are an efficient predator.
How to estimate if the pond with its presence is contributing to mosquito growth or extermination?
At best, the pond is a local source of mosquitoes.
Predators such as dragonflies can only achieve a balance: if the mosquito numbers decline, so will the dragonflies.
Frogs
If the pond cannot be covered or drained, I would encourage you to consider frogs, as Mσᶎ suggested. Worldwide, frogs are in decline, so introducing local species to the pond would seem to be a positive in sustainability terms.
But nothing comes for free: the dragonfly larvae will also be eaten.
Goldfish
While a few ordinary goldfish (or, as the Wikipedia article you linked says, guppies) will enthusiastically eat the larvae, they too will only achieve a balance. The total number of mosquitoes will be lower, but they will still be present.
Goldfish are omnivorous, so when they cannot find mosquito larvae, small crustaceans, or zooplankton, they'll eat vegetation and detritus. So they will not decline when the mosquitoes are eaten.
Unfortunately, any predator will also eat the dragonfly larvae, frogspawn, and tadpoles.
Other fish?
You do not mention your location, so we cannot know what indigenous fish could be introduced to the pond. It would have to be a species that copes well with still water.
Conclusion
In order of preference: frogs, local fish, cover or drain the pond. Avoid goldfish, since they are an introduced species and could escape.
From your link it seems likely that you're seeing a net increase in mosquitoes:
dense populations can be useful in reducing mosquito problems
I take that to mean that you need a lot of dragonflies to see a small reduction in mosquito population.
My experience is that having a vigorous frog population eliminated mosquito larvae from the ponds the frogs were in, but we still got mosquitoes from surrounding areas. Comparatively few, but enough that we still needed screens and nets. Since flying mosquitoes have no effective predators, those seem to be the two effective approaches.
I suggest either frogs or insectivorous fish in the pond, or if that's not practical, cover or remove the pond.
Filling in the pond seems excessive. Mosquito's like stagnant water, rather than flowing. Install a solar powered fountain or fall. May not help but more attractive than a filled in pond.
