Interesting question. This does depend a bit on who loses and why.
If Sanders or Warren loses, there might be the sense the party went too far left, and that someone who appears more moderate is needed.
If Biden loses, there might be the sense that someone younger/ more diverse is needed.
I don't think it'll be the people currently running. The second place finisher is likely to pretty damn old, if it's Warren, Sanders or Biden. I don't see much reason Harris, Booker or Klobuchar will do better the next time around.
Of the people who didn't run, Tammy Duckworth may be well positioned. She's a military veteran/ woman of color in Obama's old Senate seat.
The last few years haven't featured that many elections of obvious star Democrats to statewide office. Stacey Abrams and Andrew Gillum would be top contenders had they won, but they didn't win their races. Gretchen Whitmer looks the best on paper. Krysten Sinema may have a following, and has demonstrated tremendous political skill, although what worked in Arizona might not fit the US.
Some of the 2020 Senate races might also feature new contenders. Hickenlooper probably wouldn't get more buzz as a Senator than he did as a Governor, but Joe Kennedy III would be a star on day one. I could see Sara Gideon getting support.
This is a new environment where members of Congress could plausibly run. AOC would be a progressive favorite, although she likely has a ceiling (it might also be in her interest to challenge Gilibrand in the primary.) Younger African-American members of Congressional leadership Cedric Richmond and Hakeem Jeffries might have openings.
I think the most likely answer is that Dems are going to crush it in the Sunbelt states in 2022 if Trump is reelected and the nominee will probably be someone elected statewide in AZ/NC/GA/TX/maybe FL in 2020/22. I really like Mark Kelly's chances if he breaks through in AZ.