Is there a word for happiness made possible by a tragic situation?

I frequently find myself needing a word to express happiness that acknowledges a tragic or unfortunate circumstance underpinning that happiness. Preferably the word could have both adjective and verb forms. For example, "Gregory [verb-ed | felt adjective about] the balmy February day, suspecting it was yet another consequence of catastrophic and irreversible climate change."

"Bittersweet" is close, but not precisely right. It implies ambivalence rather than genuine gladness. "Schadenfreude" is also in the neighborhood, but I don't want to imply that the tragic part of the situation is what causes the pleasure. (Also, I recognize that the word may not quite exist in English, and I don't know if this is forbidden for this forum, but I'd welcome a loan word or phrase if there's a better one.)

How about an alloyed pleasure, or maybe a tarnished pleasure.

An unalloyed pleasure is a pleasure with no drawbacks, no downsides.

In this instance, we have a pleasure (in the sunny day) that was alloyed (or tarnished) by the realisation that the unseasonable warmth was caused by climate change.

"Gregory felt a tarnished pleasure in the balmy February day, suspecting it was yet another consequence of catastrophic and irreversible climate change."

"Gregory felt an alloyed pleasure in the balmy February day, suspecting it was yet another consequence of catastrophic and irreversible climate change."

"Gregory's pleasure in the balmy February day was tarnished by his suspicion that it was yet another consequence of catastrophic and irreversible climate change."

"Gregory's pleasure in the balmy February day was alloyed by his suspicion that it was yet another consequence of catastrophic and irreversible climate change."

Possibly a "silver lining?"

a sign of hope in an unfortunate or gloomy situation; a bright prospect

Source: Dictionary.com

It has a meaning of being a positive thing coming out of a negative event