Answer
This isn't practically achievable due to a fundamental difference in how the two versions implement search — Enterprise Explorer's saved searches are built directly against database columns, while the web client's searches work through OData filtering over projections, so there's no reliable way to deserialize an Apps10 saved search and translate it into an equivalent Cloud filter. The realistic path is reassessing which saved searches are actually still needed and recreating them fresh in the web client, rather than attempting an automated migration of the old serialized condition data.