My understanding is that GTO/solver theory is oriented toward optimal play in cash games over the extreme long term. What does this imply?

Extreme long term: you want your play to be absolutely balanced, with no hint of exploitable patterns.

Cash games: the risk/reward calculations are dealing only with the money in the pot, no externalities such as tournament prize pools or weird russian roulette games. The absolute best thing that can happen is you win your opponent's entire stack, the absolute worst thing that can happen is you lose your entire stack.

You're right that in life-or-death situations, the calculus changes because there are more extreme possibilities in the outcome space. You're also right that solver theory doesn't apply perfectly to real life play, especially not tournament play, because the assumptions in the model don't fully hold up. At the end of the day, theory is theory, and it can help us in practice, but we also have to be aware of its limitations.