I think you're probably right that society is likely to respond by increasing our ability to respond to natural pandemics in various ways. There's a lot of great people who are now way more interested in pandemics than they were before.
(Come to think of it, putting some thought now into how to mobilise those forces to avert the next pandemic is probably warranted, since I think there's a pretty good chance all that energy dissipates without much to show for it within a few years of this pandemic ending.)
When it comes to biorisk as a whole, the picture is less clear (though my guess is still probably positive?). There does seem to be some danger that people neglect considerations around engineered pandemics (DURC, info hazards, etc.) in their rush to tackle natural pandemics. I think a lot of work done on the latter is still useful for preventing the former, but they don't always run in the same direction, and since engineered pandemics seem to be the greatest concern from a longtermist perspective, this could be a significant concern.
I think there are sort-of four subquestions here:
1. Do these events provide evidence that we should've been more worried all along about pandemics in general (not necessarily from a longtermist/x-risk perspective)?
2. Do these events provide evidence that we should've been more worried all along about existential risk from pandemics?
3. Do these events increase the actual risk from future pandemics in general (not necessarily from a longtermist/x-risk perspective)?
4. Do these events increase the actual existential risk from future pandemics?
With that in mind, here are my wild speculations as to the answers, informed by very little actual expertise.
I'm fairly confident the answer to 3 is no. It seems quite likely to me that these events will at least somewhat decrease the actual risk from future pandemics in general, because of the "warning shot" effect you mention.
I think 4 is a very interesting question. I would guess that there's enough overlap between what's good for pandemics in general and what's good for existential risks from pandemics that these events will reduce those risks, again due to the "warning shot" effect.
I would also guess that we'll see something more like resources being added to the pool of pandemic preparedness, rather than resources being taken away from longtermist-style pandemic preparedness in order to fuel more "small scale" (by x-risk standards) or "short term" pandemic preparedness. This is partly informed by my second-hand impression that there's currently not many resources in specifically longtermist-style pandemic preparedness anyway (to the extent that the two categories are even separate).
But I could imagine being wrong about all of that.
I think the answers to 1 and 2 depend what you previously believed. I think for most people, the answer to both should be "yes" - most people seemed to have very much dismissed, or mostly just not thought about, risks from pandemics, so a very real example seems likely to remind them that things that don't usually happen really do happen sometimes.
But it seems to me that what we're seeing here is remarkably like what I've been hearing from EAs, longtermists, and biorisk people since I got into EA, from various podcasts and articles and conversations. So for these people, it might not be "new evidence", just something that fits with their existing models (which doesn't mean they expected precisely this to happen at precisely this point).