Are you sure that your Foster Claimer column (in the Animals table) is a lookup column to the Foster table?
From your photos of the available dynamic content, it seems like the data type is text. This might be why your input on the flow status was "FH-035", because it just got the text value from the record - it didn't get the data from the Foster table.
The lookup columns should have several options in the dynamic content, like in my photo where there is Value and Type. When you choose Foster Claimer (Value) it will get the GUID.
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