diff --git a/yt_dlp/jsinterp/_deno.py b/yt_dlp/jsinterp/_deno.py
index 84f19ed0a..999bc0c22 100644
--- a/yt_dlp/jsinterp/_deno.py
+++ b/yt_dlp/jsinterp/_deno.py
@@ -71,6 +71,7 @@ class DenoJSDomJSI(DenoJSI):
     _BASE_PREFERENCE = 4
     _DENO_FLAGS = ['--cached-only', '--no-prompt', '--no-check']
     _JSDOM_IMPORT_CHECKED = False
+    _JSDOM_URL = 'https://cdn.esm.sh/jsdom'
 
     @staticmethod
     def serialize_cookie(cookiejar: YoutubeDLCookieJar | None, url: str):
@@ -80,11 +81,11 @@ def serialize_cookie(cookiejar: YoutubeDLCookieJar | None, url: str):
         # https://github.com/salesforce/tough-cookie/blob/master/lib/cookie/cookie.ts
         if not cookiejar:
             return json.dumps({'cookies': []})
-        cookies: list[http.cookiejar.Cookie] = [cookie for cookie in cookiejar.get_cookies_for_url(url)]
+        cookies: list[http.cookiejar.Cookie] = list(cookiejar.get_cookies_for_url(url))
         return json.dumps({'cookies': [{
             'key': cookie.name,
             'value': cookie.value,
-            # leading dot must be removed, otherwise will fail to match
+            # leading dot of domain must be removed, otherwise will fail to match
             'domain': cookie.domain.lstrip('.') or urllib.parse.urlparse(url).hostname,
             'expires': int_or_none(cookie.expires, invscale=1000),
             'hostOnly': not cookie.domain_initial_dot,
@@ -118,7 +119,7 @@ def apply_cookies(cookiejar: YoutubeDLCookieJar | None, cookies: list[dict]):
     def _ensure_jsdom(self):
         if self._JSDOM_IMPORT_CHECKED:
             return
-        with TempFileWrapper('import jsdom from "https://cdn.esm.sh/jsdom"', suffix='.js') as js_file:
+        with TempFileWrapper(f'import jsdom from "{self._JSDOM_URL}"', suffix='.js') as js_file:
             cmd = [self.exe, 'run', js_file.name]
             self._run_deno(cmd)
         self._JSDOM_IMPORT_CHECKED = True
@@ -128,12 +129,13 @@ def execute(self, jscode, video_id=None, note='Executing JS in Deno', location='
         self._ensure_jsdom()
         callback_varname = f'__callback_{random_string()}'
         script = f'''{self._init_script};
-        import jsdom from "https://cdn.esm.sh/jsdom";
+        import jsdom from "{self._JSDOM_URL}";
         const {callback_varname} = (() => {{
             const jar = jsdom.CookieJar.deserializeSync({json.dumps(self.serialize_cookie(cookiejar, location))});
             const dom = new jsdom.JSDOM({json.dumps(str(html))}, {{
                 {'url: %s,' % json.dumps(str(location)) if location else ''}
                 cookieJar: jar,
+                runScripts: 'dangerously',
             }});
             Object.keys(dom.window).forEach((key) => {{try {{window[key] = dom.window[key]}} catch (e) {{}}}});
             delete window.jsdom;
diff --git a/yt_dlp/jsinterp/_phantomjs.py b/yt_dlp/jsinterp/_phantomjs.py
index 42aad4d3b..37b42a212 100644
--- a/yt_dlp/jsinterp/_phantomjs.py
+++ b/yt_dlp/jsinterp/_phantomjs.py
@@ -11,6 +11,7 @@
 from ..utils import (
     ExtractorError,
     Popen,
+    filter_dict,
     int_or_none,
     is_outdated_version,
     shell_quote,
@@ -87,19 +88,17 @@ def _cookie_to_dict(cookie: http.cookiejar.Cookie):
             if not cookie_dict['domain']:
                 cookie_dict['domain'] = urllib.parse.urlparse(url).hostname
                 cookie_dict['port'] = urllib.parse.urlparse(url).port
-            for key in [key for key, value in cookie_dict.items() if value is None]:
-                cookie_dict.pop(key)
             with contextlib.suppress(TypeError):
                 if (cookie.has_nonstandard_attr('httpOnly')
                         or cookie.has_nonstandard_attr('httponly')
                         or cookie.has_nonstandard_attr('HttpOnly')):
                     cookie_dict['httponly'] = True
-            return cookie_dict
+            return filter_dict(cookie_dict)
 
         cookies = cookiejar.get_cookies_for_url(url) if cookiejar else []
         return json.dumps([_cookie_to_dict(cookie) for cookie in cookies])
 
-    def _load_cookies(self, cookies_json: str, cookiejar):
+    def _load_cookies(self, cookies_json: str, cookiejar: YoutubeDLCookieJar | None):
         if not cookiejar:
             return
         cookies = json.loads(cookies_json)
@@ -110,7 +109,7 @@ def _load_cookies(self, cookies_json: str, cookiejar):
                 cookie.get('path', '/'), True,
                 cookie.get('secure', False), cookie.get('expiry'),
                 cookie.get('discard', False), None, None,
-                {'httpOnly': None} if cookie.get('httponly') is True else {}
+                {'httpOnly': None} if cookie.get('httponly') is True else {},
             ))
 
     def _execute(self, jscode: str, video_id=None, *, note='Executing JS in PhantomJS'):
@@ -139,7 +138,7 @@ def _execute_html(self, jscode: str, url: str, html: str, cookiejar, video_id=No
         html_file = TempFileWrapper(html, suffix='.html')
         cookie_file = TempFileWrapper(self._save_cookies(url, cookiejar), suffix='.json')
 
-        jscode = self._TEMPLATE.format(**{
+        jscode = self._TEMPLATE.format_map({
             'url': json.dumps(str(url)),
             'ua': json.dumps(str(self.user_agent)),
             'jscode': jscode,