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 It says earlier in the article that the volcano could warm the Earth noticeably

Other sources making that same claim:
https://eos.org/articles/tonga-eruption-may-temporarily-push-earth-closer-to-1-5c-of-warming

https://www.carbonbrief.org/tonga-volcano-eruption-raises-imminent-risk-of-temporary-1-5c-breach/

https://www.nytimes.com/2022/09/22/climate/tonga-volcano-climate.html


Here's a published paper saying it raised the atmospheric water vapor by 13%, this will last for years and will warm the surface:
https://communities.springernature.com/posts/hunga-tonga-eruption-the-most-remarkable-climatic-event-in-the-last-three-decades 
 The first article you shared says this:

"The model calculated the monthly change in Earth’s energy balance caused by the eruption and showed that water vapor could increase the average global temperature by up to 0.035°C over the next 5 years. That’s a large anomaly for a single event, but it’s not outside the usual level of noise in the climate system, Jenkins said."

The second article says this:

"The study says that, before the eruption, there was a 50-50 chance that global temperatures would exceed 1.5C above pre-industrial levels at least once by 2026. In its aftermath, the likelihood of exceeding this threshold has increased by seven percentage points – making “imminent 1.5C exceedance” more likely than not."

So although it has temporarily warmed the planet further, the major underlying cause is still because of the major excess of GHGs. So sure, maybe once all the water vapour cycles out of the stratosphere, global temperatures will cool slightly, but then again the amount of warming the water vapour may have caused is within the usual level of noise in the climate system. So even if we assume the last two winters are exceptionally mild because of the volcano, more winters like it are likely to come as the planet continues to warm. 
 Well we're in an interglacial that should continue for thousands of years, so even without human activity of any kind we would be warming 
 Sure but normal warming during interglacial periods happens slow, slow enough for life to adapt. Unlike the current rate of warming which is far exceeding historical warming periods (outside cataclysmic events like volcanism/asteroid impacts). That is the concern. 
 Absolutely, the current rate of warming is definitely a cause for concern. It's important that we address this issue and work towards finding solutions to mitigate the impacts of climate change. Thank you for bringing attention to this important issue. #ClimateChange #ActNow 
 How slow?
What's the typical rate of warming? 
 Good question, I don't know off the top of my head. Did a quick search and found this.

https://www.scientificamerican.com/article/todays-climate-change-proves-much-faster-than-changes-in-past-65-million-years/

About 10 times faster than previous warming periods in the last 65 million years. Would be cool to find papers talking about this and learn more.