WebChat v1/1.1 and WebChat v2 are mutually exclusive. It might work in the same page, but that's not a supported configuration. If they do conflict with each other, you could get creative with iframes or lazy-loading the scripts to keep them apart and only use whichever you need based on the user's activity.
Got it. So, actually the rule is you can't have: <script src="https://apps.mypurecloud.com/webchat/jsapi-v1.js" type="text/javascript"></script>
AND <script src="https://apps.mypurecloud.com/widgets/9.0/cxbus.min.js" ...>
"loaded/active" in the browser at the same time.