This seems like a good opportunity to plug the American Heritage Dictionary, which in my experience is at least a couple notches better than Merriam-Webster despite their website being stuck in 1999 (maybe that's a good thing?)
1. (often "deserts") Something that is deserved or merited, especially a punishment: They got their just deserts when the scheme was finally uncovered.
2. The state or fact of deserving reward or punishment.
Also a good opportunity to plug Webster's original English dictionary, which has a lot of very florid and evocative definitions that make it much more fun to open a dictionary https://webstersdictionary1828.com/Dictionary/desert
> DESERT, noun
>
> 1. A deserving; that which gives a right to reward or demands, or which renders liable to punishment; merit or demerit; that which entitles to a recompense of equal to the offense; good conferred, or evil done, which merits an equivalent return. A wise legislature will reward or punish men according to their deserts.
>
> 2. That which is deserved; reward or punishment merited. In a future life, every man will receive his desert
I think it's interesting that their treatment of singular they is more thorough than Merriam-Webster's, manages to address people on the dissenting side with some empathy, and still recognizes that its widespread usage[0] means it would be silly to not include that usage.
https://ahdictionary.com/word/search.html?q=desert
de·sert (dĭ-zûrt)
n.
1. (often "deserts") Something that is deserved or merited, especially a punishment: They got their just deserts when the scheme was finally uncovered.
2. The state or fact of deserving reward or punishment.