I think you're unaware of how vast vast is!
Personally, I feel vast is used to refer to things that 'appear limitless' e.g. vast desert, or when describing easily bound things - like percentages - to be almost complete.
Looking around it seems there is some debate on this, but it tends to end up suggesting the higher numbers:
https://en.wiktionary.org/wiki/vast_majority - puts vast as 75-99%
https://news.ycombinator.com/item?id=39222264 - puts vast as greater than 75% (I can't tell if the top comment is a joke or there really is some form of ANSI guidance on this).
But to find a more compelling source I've taken a look at the UK's Office for National Statistic's use of the term. While they don't seem to have guidance in their service manual (https://service-manual.ons.gov.uk/) a quick term limited search of actual ONS publications show:
* https://www.ons.gov.uk/peoplepopulationandcommunity/birthsde...
- "The vast majority (99.1%) of married couples were of the opposite sex"
- "In this bulletin, we cover families living in households, which covers the vast majority of families. " - this is high 90's by a quick google elsewhere.
* https://www.ons.gov.uk/peoplepopulationandcommunity/housing/...
- "The vast majority of households across England and Wales reported that they had central heating in 2021 (98.5%, 24.4 million)."
* https://www.ons.gov.uk/peoplepopulationandcommunity/birthsde...
- "The vast majority (93.0%) lived in care homes."
This seems to put vast in the 90%+ category. There is certainly more analysis that can be done here though, as I have only sampled and haven't looked at the vast majority of publications.
(this was fun, I don't mean to come over as pedantic)