I'm trying to change the value of the 'd' attribute on the path element but it doesn't change, no error is thrown - Demo.
HTML:
<path class="slds-progress-ring__path" data-id="slds-progress-ring-path-1" d="M 1 0 A 1 1 0 0 0 1 -2.4492935982947064e-16 L 0 0"></path>
JS:
this.template.querySelector('path[data-id=slds-progress-ring-path-1]').d = 'M 1 0 A 1 1 0 0 0 -0.8090169943749475 -0.587785252292473 L 0 0';