Filter by individual entries in comma separated lists in Google Sheets

Let's assume I had the following table:

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I want to apply a filter so that I only see the rows that contain "cat" among the comma separated "tags" in Animals column. The regular filters, of course, don't separate the possible values but instead the filter is populated with the whole string: "dog", "dog, cat", "cat, fish, bird", etc.

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Is there a way to get the filter to populate with the individual values "dog", "cat", "fish", etc.?

Alternatively, would you suggest a different table layout to achieve a similar solution, still using the manual filters? One that does not require one column per possible animal type, with boolean value.

Finally, if no solution is possible, of course there is always the option to do it with formulas, something like adding a separate cell whose input is searched in the Animals column and the corresponding entries are shown/hidden, but that is not what I am aiming for.

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