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Indexing JSON array contents
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Indexes are one-to-one.  There is one entry in the index for each row in the
table.

You are asking for an index that is many-to-one - multiple index
entries for each table row.

A Full-Text Index is basically a many-to-one index.  So if all of your
array entries really are words, you could probably get this to work
using a [Full-Text Index][1].

[1]: https://www.sqlite.org/fts5.html

But you would have to keep the full-text index up-to-date yourself, either
using triggers, or in your application.  It would not be automatic.  So,
I think the answer to your question is probably "no".