For example when I type in the search input "item", my fuzzysearch filter will not return result with name "Item". I have to type "Item" in order to filter "Item".

I also tried Contains, same result.

This would be helpful most definitely. We keep receiving Support Tickets saying the search function does not work. We then point out it's Case sensitive and close the Ticket.

Still a very nice feature though!

The fuzzysearch is case sensitive indeed, that is how it is supposed to be.
You can use the app connect formatter and make the input value as well as fuzzy search the same case, for example - lowercase:

searchColumn.lowercase().fuzzySearch(searchInput.value.lowercase())