A table variable, like any other variable, is only in scope until the end of the batch. If you run the table variable declare, then as another batch run the update, the update will fail. Same as if you first ran a declare of any other variable, then ran later a query using that variable.

You can't run this:

DECLARE @i INT

then later highlight and run this and expect it to work

SET @i = 0

Table variables have the same scoping rules as any other variable.