I wish to travel by Shinkansen from Tokyo to Kyoto in the evening of 24 February, as late as possible, keeping in mind that I will have a Japan Rail Pass and thus cannot use Nozomi trains.
The Hyperdia website is often recommended, and it shows that there is the Hikari 535 train leaving Tokyo at 20:33. However, Hikari 535 does not appear on the timetable on the operator's website.
Who is correct?
Short answer. Hyperdia is correct; you can take the Hikari 535 service at 20:33.
Long answer. Hikari 535 is an irregularly-scheduled service: it does not have a regular schedule like "every day" or "every weekday", but rather it runs only on specified days, presumably when high demand is anticipated. The timetable you linked, published on JR Central's English website, does not show such services. Hyperdia, on the other hand, does show them. One can also look at the full timetable, published on JR Central's Japanese website, and see that Hikari 535 will be running on January 14, 20, 27, and February 3, 11, 17, 24. (Schedule from March onwards not yet announced.)