Blizzard has at least acknowledged the issue: https://us.battle.net/support/en/help/article/370716
More info from other players on the thread below - seems to be an issue for characters that completed the weekly quest LAST week. If you have alts that did NOT complete the TW quest last week, you should be able to run dungeons and complete the quest as normal.
https://us.forums.blizzard.com/en/wow/t/quest-bug-an-original-journey-through-time/2037353