Are wetlands effective against climate change?
There's a misinterpretation in the &quot;steady state&quot; part, that's not what the linked paper says. It clearly states the figures are temperature dependent, and it says that in response to global warming wetlands are going to release more Methane and tries to quantify the amount. It concludes that

This finding highlights the importance of limiting global warming below 2°C to avoid substantial climate feedbacks driven by methane emissions from natural wetlands.

'Feedback' is the keyword here. Such a feedback is an accelerated response of a system to global warming. Grossly simplifying, in case of small shallow wetlands CH4 release is connected to the level of oxic and anoxic conditions, the latter expanding not only in the table of a local 'puddle' but also geographically from lower to higher latitudes with temperature and so releasing more CH4 in a warmer climate, which warms the climate and so on. But the ability of these ecosystems to bind carbon from the atmosphere drops with rising temperature, and the amount of released carbon rises.
That is by no means an argument against the conservationists who are advocating conservation and re-valuation to help sequester carbon.

This analysis can help inform practitioners and landscape managers [...] foster the worldwide implementation of wetland restoration, creation, and conservation projects for sustainable development and climate change mitigation and adaptation.

So, yes, for now wetlands are effective against climate change as long as anthropogenic global warming is limited.