If the presence of dimethyl sulphide is confirmed, what would the next steps be? Presumably sending a probe would not be feasible in any foreseeable timeframe?
So the next step would be to build better and better telescopes to observe these planets, learn about their composition, and inspire people to study and fund the sciences.
There are some proposals of how to build fast probes that could visit very close star systems that could maybe, maybe reach a the 4 LY to Proxima Centuri within a human lifetime. But 124 LY is so far that even the Starshot proposal would take nearly 800 years to receive data back.
So the short term solution (in the order of decades) is improve the observation capabilities. More observations with the JWST should give a better idea what the next iteration of a space telescope for this job should be and give some motivation of accelerating building such a telescope. JWST itself took decades to build and deploy. It would be remarkable, if an improved telescope could be deployed in a 10 year time frame. Of course, an operational Starship would help a lot with that, as a lot of effort for JWST was the complex deployment mechanism.
With global resources we can do it easily but the people in charge of our countries wouldn't have a job if they didn't invent fake boogeymen to waste cash on instead.
We have plenty of starshot proposals that are incredibly cheap compared to other things: https://en.wikipedia.org/wiki/Breakthrough_Starshot
How do you propose getting a probe to something 120 light years away and getting an answer within a human lifetime, unless you're going for a ride on the probe? Do you have some new physics?
These are very real ideas with very real engineering designs by incredibly smart people. It's not sci-fi mate, we can actually do this with enough wherewithal.