Event Countdown block timezone is unclear and inconsistent

### Impacted plugin

Jetpack

### Quick summary

I tried to add an instance of the Event Countdown block to a post. It was very unclear what timezone it was interpreting the input in, and as far as I can tell it was wrong.

### Steps to reproduce

1. Have your timezone set to America/New York. Not sure if this is your browser, or your blog, or what.
2. Add an Event Countdown block.
3. Try to set an event for a specific UTC time a few months in the future, across the next DST change.
5. Publish, then calculate the time of the target event based on what's shown in the block.

### A clear and concise description of what you expected to happen.

Ideally, a clear indication in the picker and in the button exactly what timezone is being used. Even better if I can select the timezone.

### What actually happened

No timezone is indicated in the picker or in the button. After entering a time and dismissing the picker, the button shows a time 1 hour off from what was entered.

It appears that the picker interprets the entered time based on the current UTC offset, not the offset that will be in effect on the selected date. The button displays the time using the offset that will be in effect on the selected date, and the block itself displays the countdown to what the button displays.

### Impact

All

### Available workarounds?

Yes, easy to implement

### Platform (Simple and/or Atomic)

Simple, Atomic, Self-hosted

### Logs or notes

_No response_

No file or test is named in the report. Start by reproducing the Event Countdown block flow across a daylight-saving transition, then trace the picker and displayed button time; done means the active timezone is clear and the selected event time remains consistent across the picker, button, and countdown.

Written by the indexing model from the issue text.