05AB1E, 3 bytes

ε¢W

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How?

^{Note: Uses the current interpretation of https://codegolf.meta.stackexchange.com/a/2216/52210 that seems to be being used, that not only may a string be provided as a list of characters but that it may be provided as a list of single-character strings.}

ε¢W - inputs are: words (list of lists of strings of length one);                  wordsearch (space separated string)ε   - for each word:¢  -   count occurrences of each length-one-string in the wordsearch  W -   minimum

Original 4 that does not use a list of lists of strings for the words...

ε€¢W

Try it online!

How?

ε€¢W - inputs are: words (list of strings); wordsearch (space separated string)ε    - for each word:€   -   for each letter:¢  -     count occurrences in the wordsearch   W -   minimum

^{* Taking the words as a list of lists of strings would work, but seems like pre-processing rather than loose IO to me.}