It may already have. The question is is 725 LY far enough away that we don't blow up too?
This [1] article discusses a closer one that may have been responsible for a mass extinction.
[0] https://astronomy.com/news/2020/02/when-betelgeuse-goes-supe...
[1] https://www.discovermagazine.com/the-sciences/a-nearby-super...
Edit: Wikipedia says < 1000 LY would have noticeable effects on life on Earth: https://en.wikipedia.org/wiki/Near-Earth_supernova
Betelgeuse will explode in a faint Type II-P supernova, which is the least dangerous type. The thing to really be worried about with supernova are gamma ray bursts, which require low metallicity stars of at least 120 solar masses. Betelgeuse is a high metallicity star with about 15 solar masses. So it's nowhere even in the ballpark of producing a gamma ray burst.
Look at this graph:
https://upload.wikimedia.org/wikipedia/commons/5/5a/Comparat...
Betelgeuse will be the blue line that peaks the lowest and plateaus out. (the P is Type II-P stands for "plateau") This is a logarithmic plot, so the brightest supernova are like 40 times as bright as Betelgeuse's supernova will be. Furthermore, this is just visual light; in terms of gamma rays, while normal supernova are bright in gamma rays, gamma ray bursts are many orders of magnitude brighter.
When Betelgeuse goes supernova, no species will go extinct, no crops will fail, no uptick in cancer will happen. It might dork up some migration patterns and mess with particularly precarious food chains, but the effects will be minor, especially compared to the catastrophic damage humanity is doing to the environment.
The phrase I was referring to was "have noticeable effects on Earth's biosphere", not "we will notice it". The article explains:
Historically, each near-Earth supernova explosion has been associated with a global warming of around 3–4 °C (5–7 °F). An estimated 20 supernova explosions have happened within 300 pc of the Earth over the last 11 million years. Type II supernova explosions are expected to occur in active star-forming regions, with 12 such OB associations being located within 650 pc of the Earth. At present, there are six near-Earth supernova candidates within 300 pc.
That seems like quite a bit more just seeing something in the sky or seeing a few species get their migration patterns messed up. And re: gamma ray bursts, I do agree they would be bad if they occurred, but you might notice I didn't mention them either. My first worry was about fast-moving particles, which you didn't mention anything about. Why would those not be problematic?
You might very well be right about Betelgeuse specifically, but I'm guessing you're relying on more information because I just can't deduce it from the information I'm seeing.
Assume Betelgeuse explodes in a typical Type II-P supernova. This will give it an absolute magnitude in the ballpark of -16.5, call it an even -17. Betelgeuse is approximately 220 parsecs away, which would give an apparent magnitude of 5*(log10(220) - 1) - 17 = -10.3. The full moon is -12.9, so is approximately 10 times as bright.
Specifically regarding energetic particles, the amount of material blown out at relativistic speeds from a II-P supernova is negligible. The high energy interactions happen way inside the star's envelope. The high energy stuff all gets absorbed and re-emitted as lower energy light. The plateau in the light curve of a Type II-P supernova is caused because the outer layers are completely opaque and are trapping energy in the interior.
That's actually the reason I keep contrasting Type II-P with gamma ray bursts. In those events, the outer layers have been stripped away, and we have a direct view on the high energy interactions happening in and around the collapsing core. There is no material to block it, so everything about it is more intense; there are vastly more high energy particles spilling out as cosmic rays, the peak brightness is much brighter, and the light that is emitted is much hotter.
Basically, supernova are fundamentally different from each other. They're a family of phenomena, not just one thing. A gamma ray burst directed at Earth will be catastrophic at 1000ly; (which is why the article talks about supernova up to 1000ly) a Type II-P supernova at 10ly will be comparably catastrophic, but simply won't register at 700ly.