If I understand correctly, jQuery works fine system wide. jQuery UI (which includes autocomplete) works but only from within a blade context, and not from within a Vue context.
How are you incorporating jQuery UI into your system? Via CDN? Local install + require() call?
I haven't used jQuery in quite some time now, and I haven't run into this specific issue. I have however, encountered similar issues where some of my dependencies were accessible via blade, but not from within my Vue components.
What ended up solving it for me was to ensure that when requiring the 3rd party library, that it gets assigned as a top level variable (directly into the window). Using the Axios dependency as an Example:
window.axios = require('axios');
^^ would go in app.js/bootstrap.js (wherever you normally require your dependencies)
Not sure if this helps, but I'm hoping it gets you pointed in the right direction at least.