how do I upgrade a Windows 2012 domain

.-->how can I update this network to a supported "environment"
Please elaborate.
Do you want to upgrade to 2012 R2 or 2016?

What is the current OS of all your domain controllers?
If all run at least 2012 R2 you can upgrade forest and domain functional level to 2012 R2.
If you still have domain controllers with 2012 or below you'll have to replace them first.

Also check if SYSVOL replication has been witched to DFSR
https://techcommunity.microsoft.com/t5/storage-at-microsoft/streamlined-migration-of-frs-to-dfsr-sysvol/ba-p/425405

On what basis are you asserting that you are in an Unsupported environment?
Are you trying to install an application that tells you your environment is unsupported?

MAS asked the what question.

More detail please to get clarity on the issue at hand.

My domain is 2012 not R2.   I see that it has extended life support thru 2023 so unsupported is not an accurate statement. I am going to replace the domain controller, my question is, moving from a 2012 DC, how "high" can I go.

AD Functional Levels have not changed since Server 2016.

We just set up a greenfield AD Forest. "7" is still the functional level for the Server 2022 DCs.

If there is a need to migrate AD Replication from FRS then: https://blog.mpecsinc.com/2019/05/15/server-2019-and-adds-frs-not-supported-migrate-to-dfsr/.

It's fairly simple though it may take a bit of time depending on the AD Replication Topology.

The Server OS is 2012 R2 the AD functional level does not include that marker.
Commonly no vendor places a restriction based on what your AD functional level is.

Vendor supported/unsupported is based on which OS, HW they tested with their product and know it works versus untested and they do not want to be providing the support personnel if something does not work for you.

If your system/working environment physical or virtualized?
If you are buying Volume license software, you can buy the 2022 while instealling/deplying the 2019 that had time to get the bugs worked out.
The same way vendors lag behind, business would not want to be the guinea pigs of the new OS to discover which of their essential functions are impacted by the new OS.
I.e. since you are going from 2012 to 2019/2022. web based application/settings are more granular on the 2019/2022 for IIS and you might find your web app, in need of fixes.

Licensing also changed since 2012. Note: if you go to 2019/2022 without software assurance on your prior CAL purchases, you will need to buy new ones for the 2019/2022 version....