Is your ProcessWire instance installed in the root web directory or somewhere else?
The only noticible change I find in your code examle is the directory within the script tag:
<script nomodule type='text/javascript' src='.../site/modules/PrivacyWire/js/PrivacyWire_legacy.js'>
Usually the src attribute starts directly with '/site/' instead of '.../site/'
<style>.privacywire{position:fixed;bottom:-250%;left:0;right:0;box-shadow:0 -1px 3px rgba(0,0,0,.3);opacity:0;background:#fff;z-index:1;padding:1rem;transition:bottom .3s ease-in,opacity .3s ease}.show-banner .privacywire-banner,.show-message .privacywire-message,.show-options .privacywire-options{bottom:0;opacity:1}.privacywire-header{font-weight:700}.privacywire-ask-consent-blueprint,.privacywire button[hidden],[data-ask-consent-rendered="1"]{display:none}</style>
<script>var PrivacyWireSettings={"version":1,"dnt":"0","customFunction":"","messageTimeout":1500,"consentByClass":"1","cookieGroups":{"necessary":"Necessary","functional":"Functional","statistics":"Statistics","marketing":"Marketing","external_media":"External Media"}};</script>
<script type='module' src='/site/modules/Privacywire/js/PrivacyWire.js'></script>
<script nomodule type='text/javascript' src='/site/modules/Privacywire/js/ie_polyfill.js'></script>
<script nomodule type='text/javascript' src='/site/modules/Privacywire/js/PrivacyWire_legacy.js'></script>