fix: correctly handle falsy values of style directives in SSR mode

fixes #11044

.changeset/good-roses-argue.md

@@ -0,0 +1,5 @@
+---
+"svelte": patch
+---
+
+fix: correctly handle falsy values of style directives in SSR mode

packages/svelte/src/internal/server/index.js

@@ -354,7 +354,7 @@ export function stringify(value) {
 /** @param {Record<string, string>} style_object */
 function style_object_to_string(style_object) {
 	return Object.keys(style_object)
-		.filter(/** @param {any} key */ (key) => style_object[key])
+		.filter(/** @param {any} key */ (key) => style_object[key] != null && style_object[key] !== '')
 		.map(/** @param {any} key */ (key) => `${key}: ${escape_html(style_object[key], true)};`)
 		.join(' ');
 }

packages/svelte/tests/runtime-legacy/samples/inline-style-directive-falsy-value/_config.js

@@ -0,0 +1,11 @@
+import { test } from '../../test';
+
+export default test({
+	html: `
+		<p style="--a: 0;"></p>
+		<p style="--b: false;"></p>
+		<p></p>
+		<p></p>
+		<p></p>
+	`
+});

packages/svelte/tests/runtime-legacy/samples/inline-style-directive-falsy-value/main.svelte

@@ -0,0 +1,5 @@
+<p style:--a={0}></p>
+<p style:--b={false}></p>
+<p style:--c=""></p>
+<p style:--d={undefined}></p>
+<p style:--e={null}></p>