Describe the bug

When displaying the time in the calendar, a hint was added in #23400 so the user would know what timezone the post was being schedule in.

The issue is it now appears that the time being selected is the user's time and not the server time.

To reproduce
Steps to reproduce the behavior:

1. Set the site time to a different timezone, this example site set to EDT
2. Create a new post and schedule the post time
3. Notice the hint shown is EDT, but the time picked is in PDT

Expected behavior

The time shown should match the hint of what time zone it is being set to.

Screenshots

Related trac ticket: https://core.trac.wordpress.org/ticket/50624