Black's Law Dictionary (5th edition 1979) states that "Liquidated" means
Ascertained; determined; fixed; settled; made clear or manifest.
This is the sense of the term in which damages are "liquidated" by a liquidated damages term in a contract or statute. The damages are settled by a contractual determine rather than being "unliquidated" (i.e. uncertain or unresolved or undetermined.)
The sense of the word meaning sold or reduced to money, is derivative of this prior and more fundamental sense of the word. When assets or an estate are reduced to money their fair market value is fixed or settled.
How a word meaning "liquid" came to mean "make clear" when modified is speculative (given what my brief research uncovered), but I think that are some very plausible paths by which that could have happened.
According to Oxford Languages:
mid 16th century (in the sense ‘set out (accounts) clearly’): from
medieval Latin liquidat- ‘made clear’, from the verb liquidare, from
Latin liquidus (see liquid). liquidate (sense 1) was influenced by
Italian liquidare and French liquider, liquidate (sense 2) by Russian
A second online dictionary source states:
1570s, of accounts, "to reduce to order, to set out clearly" (a sense
now obsolete), from Late Latin or Medieval Latin liquidatus, past
participle of liquidare "to melt, make liquid, make clear, clarify,"
from Latin liquidus "fluid, liquid, moist" (see liquid (adj.)). Sense
of "clear away" (a debt) first recorded 1755. The meaning "wipe out,
kill" is from 1924, possibly from Russian likvidirovat, ultimately
from the Latin word. Related: Liquidated; liquidating.
English.StackExchange has some answers of essentially the same question that doesn't shed much more light on the matter but one excerpt is notable:
The meaning is already present in the Latin liquidus which means both
"liquid" and "clear, evident".
This obviously comes from liquids being limpid (transparent). Limpid
by the way (another Latin cognate, originally from Oscan origin) gives
Spanish limpido and limpiar.
Also liquare means "to filter". So that the idea of transparency and
purity is already strongly associated with liquids in Latin.