SW WA Salish root ʔúm̓ and Chinuk Wawa mékʰmək: a shared Indigenous concept?
Whether or not we claim that it came from Salish, the Chinook Jargon use of a single verb for both ‘drink’ and ‘eat’ has a close parallel in local tribal languages.
The Lower Chehalis Salish root ʔúm̓ refers to giving either food or drink (viz. ʔumsqʷúʔəcaʔ ‘give me water!’ and ʔúm̓ən tiʔ ‘they fed them’).

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Lower Chehalis is one of the parent languages of the Jargon, right along with Lower Chinookan and English.
Maybe you already see the similarity in meaning between ʔúm̓ and early (and Northern Dialect) Chinuk Wawa’s mə́kʰmək ‘to eat; to drink’. (Later, Southern Dialect has a separate word loqa for ‘drink’.)
So we suspect an Indigenous influence here, as in countless other features of Chinook Jargon.

I’d be careful here.
Pidgins are notorious for their small number of lexemes, leading to heavy use of compounding to express notions which are (typically) expressed by single lexemes in non-pidgin languages. This also means that many pidgin lexemes will have a broader semantic range than they had in their (non-pidgin) source language. For a single pidgin lexeme to mean “eat” and “drink” is unsurprising, whether the L1’s of the pidgin users use a single such lexeme with both meanings or not. Now, find an instance of semantic narrowing in CW or indeed any pidgin which matches the semantics of the users’ L1’s, and then you will have a MUCH stronger case.
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