My understanding is that this material remains toxic to life for thousands, to tens of thousands of years.

Safe means that it's stored such that there's no harm to the environment for that lifetime.

In all "bury it" scenarios, the place where the waste is buried will be subject to change resulting in water, air, able to interact with that waste when normal tectonic and erosion processes do their thing.

I keep coming back to this to reply but I cant really figure out how to tackle it. Theres so much of a particular view of the world in each statement.

How do you think spent uranium interacts with the environment?

There's an estimated 4.5 billion tons of uranium dissolved in seawater. Naturally occurring. I honestly think we missed a trick when we outlawed dumping in the ocean, there's basically no way for human generated nuclear waste to even move the needle on ocean sources.

Lets say I take you completely at face value. Every notion of yours comes to pass. We cask it, and leave it in an underground vault. 9999 years later, a cask fails. Whats the issue? Are you using that vault as a busy thoroughfare? Its still in a big hole in the ground. Maybe theres an earthquake? And the vault shears a little. What is the radiation now doing in your mind that makes it dangerous? TBH we shouldnt leave signs warning people to stay away, we should leave a concrete recipe behind on all the signage.

There's life thriving in Pripyat just past the big concrete dome. There's a war going on there.

Tectonic and erosion processes take place over millions of years, so they aren't an issue for waste that's only dangerous for tens of thousands of years.