Is Azure Managed Disks enough to ensure high-durability for a database?
But I want to ensure that data that gets stored will not be lost, i.e. is durably stored with very high probability.

Yes.  It could happen, but it's an extremely low-probability event, and there's many other low-probability events that are more likely.  It's vastly more likely that your data will be lost due to a guest OS driver problems, human error, or malware than Azure would lose data on a disk.
See:
LRS provides at least 99.999999999% (11 nines) durability of objects over a given year.

Azure Storage redundancy
And whatever that means, you can bet that a lot of things would have to go very wrong to lose a disk.
If you are happy recovering from backups for those other scenarios, you should be fine.`