The link mentions 100 meters depth. Without being an expert that sounds deep enough to withstand hurricanes and such.
However 100m depth? For a structure _that_ size, which I think might contain high vacuum, let alone systems that might need humans to service when they break? What is the feasibility of that problem?
As mentioned in the linked presentation, they envision using interconnected 300m (1000ft) long segments that can be changed using ROVs, using technology that's already available for underwater pipelines.
Also mentioned is that the LHC cryostats, some nice illustrations here[1], are very nearly neutrally buoyant. Given these would be built similarly, they wouldn't need significant infrastructure to keep them in place.
So no humans would need to go down there, if something breaks they could just replace the broken segment(s) and fix the broken one(s) on the surface.
"So no humans would need to go down there, if something breaks they could just replace the broken segment(s) and fix the broken one(s) on the surface."
This frankly is not possible. Colliders need constant maintenance. The "Collider in the Sea" is not a real proposal.
Presumably the plan would be you're actually building a the collider tunnel much like CERN under water, so effectively a very long pressure structure. This...probably isn't super-unreasonable for a static structure where you avoid the cost of excavation - i.e. it depends on how different in diameter from something like the Nordstream pipelines you'd be going.
Using established technology from offshore industry it's supposedly not as crazy nor costly as one might first imagine.
There was a nice and fairly accessible talk[2] given at Perimeter Institute, which gave some background and went into this and the FCC.
[1]: https://arl.physics.tamu.edu/research/collider-in-the-sea/
[2]: https://pirsa.org/20100056