AD is LDAP+Kerberos, which has existed in the Unix/Linux world long before Microsoft bastardized it. So pick any of half a dozen LDAP server implementations and any of 3 or 4 Kerberos implementations and use those. If you want point-and-click/drool interfaces, use FreeIPA. If you really want it to look like AD, use Samba 4. Even Windows boxes will hardly know the difference.

Group policies don't exist and won't ever exist on Linux. Group policies are LDAP entries that are copied on system boot and user login into their respective parts of the local registry. Software may then read, interpret and use those registry entries. On Linux that wouldn't work for numerous reasons. First, on a multiuser system rebooting to apply configuration changes is not viable. On windows that's apparently fine because its single-user anyways, and reboots are an accepted fact of life. Also, to apply a system policy that is intended to limit what a user could do, asking the user's software nicely via registry entries is stupid and insecure. Lots of software won't even read the registry and have group policies that it will obey. Want to get around an Internet Explorer Group policy? Use Chrome or Firefox!

So what you do instead on Linux is: If it's just configuration, just copy it over, using the usual text configuration formats that are common on Linux. There are lots of tools to do this, starting from simple hack jobs like using scp to full configuration management systems like ansible or puppet. The "group" part is handled by those systems as part of their function, you can easily group/subgroup/discover/inventory/parameterize. If it's policy, so you want to restrict what a user can do, you use the higher-privileged layers of the system to put in actual restrictions, not just "group policy" suggestions. You can configure the user's home directory to be mounted noexec, so software execution after an unauthorized installation is impossible. You can put them in containers, namespaces, limit their resources and system access using cgroups, filesystem permissions, and more fine-grained permission systems like SELinux. If you are so inclined, you can forbid the user from opening files starting with the letter 'f', using eBPF syscall filters (this will of course break everything, but I needed a stupid example ;). All those can also be configured with your configuration management system of choice.

Just as a comparison: Our windows team needs 3h just to re-image a laptop, just for windows. After that, all the software needs to be reinstalled, all the data copied over. Then, after 2 days and 10 reboots or something, it will have picked up all the policies, updates and things and maybe be usable. Our Linux installation takes 45 minutes. Including all the software that was previously assigned to this system, including all the settings. It will be fully updated, configured and usable after the first reboot.