- Show the timezone name/descriptor if I select a city (yes, it already says 'GMT+X', but it would be helpful to have the local timezone name of that city as well) - Somehow select a time for a different day. E.g. if I want to compare the times for the 22nd of October 2024 instead of today (Countries/Cities/Regions swap timezones x-times a year, on different days)

I was thinking it would be cool to add another slider for day of the year. That way you can see how the differences change as local timezones roll through their own daylight savings time or other adjustments. For example, right now Asuncion Paraguay is +3 hours ahead of Chicago U.S. but in April it will be only one hour ahead.

Link sharing would be useful. Here is a site similar to yours, albeit not as pretty. https://podfeet.com/webapps/time-shifter-clock/