Given that, throughout history, a handful of volcanic eruptions have triggered periods of global cooling, will global warming become a non-issue if a particularly large volcano happens to erupt in the next few years?

I think it could solve all of our problems so that we are never inconvenienced by having to do anything. To promote the success of sitting around waiting for a volcano to save us while our portfolios appreciate, I've started a Wiccan druid circle for attuning our spirits to the volcano god Pele.

Not meaningfully.

Volcanic winters only last a few years. The largest ones are estimated to only have a few degrees effect on global temperatures, so we could temporarily be in 1980s climate before returning after 3-5 years to an even hotter one than ever.

The climb would probably accelerated by the inevitable policy reversals by climate change deniers who would take hold of the temporary rapid reversal of global warming to burn as much fossil fuels while they have the chance

A volcanic eruption by itself can trigger some cooling by reflecting a bunch of sunlight off the dust/gas that's in the volcano emissions. Those cooling periods last a couple years.

In terms of having a longer cooling period with volcanoes, what happened historically was you had several volcanic eruptions in a row that caused something else to happen entirely -- sea ice restoration which caused a feedback loop. Generally, more sea ice begets more sea ice (Effectively, you're trading black ocean surface that absorbs light/heat for white ice that reflects light/heat. And so you get this feedback loop, more ice, cooler temps, even more ice) Anyway, The More You Know Star about some climate history stuff. (One issue with global warming is we're nearing the opposite end of that feedback loop, where less sea ice begets less sea ice and everything melts super fast. For shorthand, you can say that the temperature of Earth is likely rising as slowly as it will during the rest of our lifetimes. The ice is melting as slowly as it will for the rest of our lifetime. The sea level is rising as slowly as it will for the rest of our lifetime. etc)

The other thing to point out here is that volcanic emissions just mask warming caused by greenhouse gasses (ignoring the ability to start feedback loops). At the extreme end, for example, human IQ starts to suffer around 1,000 parts per million of carbon dioxide, so no matter what the temperature is in that scenario it's likely a decent idea to deal with carbon dioxide.

The sub text is generally "people are to blame" and "people must buy into a solution" with symbolic action.

Pointing out that were in an iceage and the planet used to be warmer or the role of volcanos isn't playing ball with the narrative.

they (volcanos) also released so much carbon dioxide that we got a "Great Die Off", and walked the line between livable atmosphere and utterly-toxic-to-everything

volcanos ain't the answer, mate