OK, so we didn't find a direct way to do it. However, we believe that the following approach should work for normal and community usage. In essence we implemented a component with navigation mixin then used something like:

    this[NavigationMixin.GenerateUrl]({
			type: 'standard__navItemPage',
			attributes: {
				apiName: "customTabName",
			},
			// query string parameters
			state: {
				c__showPanel: 'true' // Value must be a string
			}
		}).then(url => {
			window.open(url)
		});

Importantly, this doesn't actually navigate directly to a Visualforce page, but rather to a custom tab into which the page is placed (clearly the tab needs to be accessible by the user). Note, too, that the "query string parameters" included seem to be correctly available within the Visualforce page and the use of window.open allows the URL to be opened in a separate tab or window within the browser.