In that hypothetical of running 2 instances of Stockfish against one another on a modern laptop, with the key difference being minutes of compute time, it'd probably be very close to 100% of draws. Depending on how many games you run. So, if you run a million games, there's probably some outliers. If you run a hundred, maybe not.
When it comes to actually solved positions, the 7-piece tables take around 1TB of RAM to even run. These tablebases are used by Stockfish when you actually want to run it at peak strength. [3]
[0]: https://tcec-chess.com [1]: https://lichess.org/broadcast/tcec-s28-leagues--superfinal/m... [2]: https://lczero.org [3]: https://github.com/syzygy1/tb
I remember hearing that starting position is so draw-ish that it's not practical anymore
Chess is a 2 player game of perfect, finite information, so by Zermelo's theorem either one side always wins with optimal play or it's a draw with optimal play. The argument from the Discord person simply says that Stockfish computationally can't come up with a way to beat itself. Whether this is true (and it really sounds like a question about depth in search) is separate from whether the game itself is solved, and it very much is not.
Solving chess would be a table that simply lists out the optimal strategy at every node in the game tree. Since this is computationally infeasible, we will certainly never solve chess absent some as yet unknown advance in computation.
In the TCEC game, I see "2. f4?!", so I'm guessing Stockfish was forced to played some specific opening, i.e. it was forced to make a mistake.
For what it's worth, Stockfish wins the rematch also. https://tcec-chess.com/#game=13&round=fl&season=cup16
It's also almost certainly the case, in that I don't know why you would do it, that Stockfish given the black pieces and extensive pondering would be meaningfully better than Stockfish with a time capped move order. Most games are going to be draws so practically it would take awhile to determine this.
I'm of the view that the actual answer for chess is "It's a draw with optimal play."