Taskwarrior supports spaces in projects:

task add foo project:'bar baz'

In Vit, this will tab complete but without escaping the space character. This happens everywhere that project completions exist, such as for "modify project":

Project: bar baz

In this example, Vit will change the project to "bar" and drop "baz" as extra input.
The workaround is to add a backslash escape, same as you would do if you wanted taskwarrior to parse multi-word field as single token (project, duration, string substitution).

More generally, maybe this is a bug for all completions, they currently only work with single words?