As you observed, Jdbi does not parse bound parameters inside quotes. This is intentional.
Even if we did parse it, JDBC wouldn't recognize the bound parameter: WHERE name LIKE '%:query%' would be parsed to WHERE name LIKE '%?%', which JDBC would just treat as a literal varchar anyway. And then you'd have another problem: bound parameters after the LIKE clause would be applied off-by-one by JDBC, because of the LIKE parameter it didn't recognize.
I agree it's a bit annoying, and I'm open to introducing API to make this more approachable. Maybe a bindLike(), bindLikePrefix(), and bindLikeSuffix() method, and matching SQL object annotations? Or some other names.
Would you care to open a bug on GitHub?