This is expected. WAF has added support for websockets in recent releases, but Web Filtering has not. Web Filtering supports HTTP, HTTPS, and FTP protocols only. You need to create a bypass for this site.
In Website overrides, create a TAG named "Bypass All" and assign it to your website.
In Exceptions, create an exception object, check all the boxes, and configure it for "Going to websites tagged as" tag="Bypass All".
This approach worked for me for both Standard and Transparent mode. My best guess is that your first attempt at an exception either had a Regex error or insufficent exceptions.
Check Your Logs
You have not mentioned what your logs say, which implies that you have not been looking at them. This is a mistake. The logs will tell you what Filter Profile, Policy, and Exceptions were applied, what action was taken (id and name), and result (statuscode="value" and error="value".
Exceptions may not work in this situation
There is a possibility that Web Filter cannot handle the unrecognized wss protocol, triggering a failure before the exception can be applied. The logs should help you know if this is the case. If it is, then you will have to bypass by other means:
The exception object is preferable because it solves the problem in both modes, and it does so based on URL. This means that IP addresses do not need to be known in advance.
RegEx may be the right solution
You could create a bypass-all exception to ignore and websocket traffic. I think the regex would be: $wss:\/\/
On the other hand, you may want to allow websockets only as needed. If so, then you create exceptions for specific host names, and let the others be blocked by default.
RegEx vs WebSites with Tags
The UTM RegEx logic works. The problem is ensuring that your RegEx does what you want, with neither unwanted matches nor unwanted mismatches. I started abandoning RegEx after an unwanted URL was allowed because of a subtle RegEx mistake (a host name was allowed, but it also allowed a URL with the host name embedded in the querystring.
Tags provide several benefits that I love:
Limitations to consider: