iOS 16 users only can use Jailbreak Repo extractor methods and virtual Jailbreak tools to install Cydia / Sileo and other Jailbreak features.

This is the recommended method to install lite versions of Cydia / Install Sileo and the most popular jailbreak features for iOS 16.
Also repo extractor latest iPhone 13 Jailbreak and iPhone 12 Jailbreak.

Zeon is the most famous repo extractor tool for the iOS 16 version. Tap the below link to install the Zeon Repo extractor.

Hexxa is another available repo extracting method to Jailbreak iPhone and iPad running iOS 16 version.

Bregxi Jailbreak repo extracting method also supports iOS 16 jailbreak.

iOS 16 users can install Semi Cydia after extracting the Checkra1n and Unc0ver virtual jailbreak tools with this method.
Before extracting virtual jailbreak repos, you must install Zeon Repo Extractor first.
Then you must extract the below repo URLs to install Cydia lite version.

iOS 16 users can install Cydia ( Virtual ) from two different methods.

The first one is by extracting the virtual jailbreak tools. Use this guide to install Cydia by extracting the Repo URL.

The second method is to install Cydia directly from the zJailbreak app store. Install zJailbreak from here.

Zylon is another method to install the lite version of Cydia. Zylon Cydia supports every iOS and iPad device running iOS 16.

Taurine Jailbreak is the only latest tool that supports installing Sileo. But without Taurine Jailbreak tool support, iOS 16 users can install the Semi version of Sileo.

Install the zJailbreak tool from here and then install Sileo.

Zeon is another method to install Sileo for iOS 16. Install Zeon from the below link and then install Sileo from Zeon without PC jailbreak method.

Third-party tweak app stores are the other available method to install jailbreak features for iOS 16 and iPadOS 16 versions. On this page, we listed a few app stores and you can view the full list that supports iOS 16.

Zeon is the most famous app store for the iOS 16 version. Tap the below link to install the Zeon app store.

zJailbreak is the most famous third-party app store in the iOS 15 version. Now, zJailbreak also supports iOS 16 and iPadOS 16.

Appcake also supports iOS 16 version. If you are jailbroken user, you can use the Appcake Cydia version to install jailbreak features.
Non-jailbroken users can install Appcake from the below link.

Appvalley also supports iOS 16 and iPadOS 16 versions. Tap the below link to install the Appvalley app store.

With the below websites, iOS 16 users can install most of Jailbreak Cydia features without having a Cydia application installed.

AltStore and sideloadly IPA sideload methods now support the iOS 16 version. Both the methods support Windows and macOS operating systems. Also supports every iPhone and iPad models running iOS 16 and iPadOS 16 versions.
AltStore Sideload method - Written & Video Guide
Sideloadly method - Written and video guide
Best IPA for AltStore & Sideloadly - Download

With the ShowLive and Glance methods, iOS 16 users can change the Home Screen theme and Lock Screen theme. But these both methods do not support the iPadOS versions.
Both ShowLive and Glance support every iPhone model running iOS 16
ShowLive - Written guide
Glance - Written guide

With the Siri automation method. iOS 16 and iPad16 users can change Home Screen icons. Even you can add your own image from the gallery.
How to change the home Screen icon - Written Guide

The Cydia tweaks are not the only way to change Lock Screen buttons. Japanese website released a new way to change it without Jailbreaking and without installing any app. Even this method supports every iPhone and iPad devices running 16.
How to change Lock Screen Buttons - Guide

Japanse Jailbreak tweak creator released a brand new method to change the Home Screen dock without Jailbreak your Devices. Even you do not need to install any application to change Home Screen Dock.
How to change Home Screen Dock - Guide

Changing the boring home screen theme is one of the main purposes of Jailbreaking. But still, iPhone and iPad users can install a new theme for Home Screen without jailbreaking the Devices. From the below methods, iOS 16 users can change the Home Screen theme to newone.
Ela Themes - Can install from the Zeon App - Install
Ela Themes official Website - Link

Yes, some jailbreak experts are working on releasing a full jailbreak for the latest iOS 16 and iPadOS 16 versions. Here is the latest news about iOS 16 Jailbreak.

FilzaEscaped15 is the latest tool that supports to access the iOS file system. But FilzaEscaped15 still does not support the latest iOS 16 version. If you are iOS 15 to 15.5 versions, you can use it to accused the file System.
Without a PC is the easiest method to install IPA files to iOS Devices, but these online IPA files can be revoked anytime. In this case, you can use Sideload method to install FilzaEscaped15.

Cheyote is the renamed version of Taurine15 Jailbreak. According to the Developers, Cheyote Jailbreak does not support iOS 16 Jailbreak.
If you want to use the Cheyote jailbreak tool, you must downgrade the iOS 16 version to iOS 15.5 version.

According to developers, Taurine Jailbreak coming soon for the iOS 15 to 15.1 version but not for the latest iOS 16 version.
If you are using Jailbroken Devices, please do not upgrade to the latest 16 version. If you want to use iOS 16 features, you can use alternative Cydia features for it.
According to some experts, Apple has copied these new features from the Jailbreak community.

Checkra1n jailbreak currently supports up to iOS 14.8.1 jailbreak. At this time, checkra1n jailbreak developers working to release checkra1n for iOS 16 jailbreak.
If you have seen Checkra1n jailbreak for iOS 16 it might be fake. We will update you once release Checkra1n Jailbreak for iOS 16.

Permasigner is a newly released method that bypasses automatic IPA revoke. With the Permasigner tool, users can sign IPA files permanently.
But you should jailbreak your Devices to use this method. So once jailbreak iOS 16, you can use this method.

Once upgrade you your running iOS version to the iOS 16 version, you will lose the downgrade possibility to an older version. Only you can downgrade it to the previous version. So if you are running older iOS version such as iOS 15 to 15.2, better to stay as it is and waits for jailbreak.

With iOS 16 releases, Apple unlived many new features. But most of them were copied from the jailbreak community.
So, jailbroken users still can feel iOS 16 features without updating to the iOS 16 or iPadOS 16 version.