Will server to server migration work cross-domain/cross-active directory?

Back in 2016, I upgraded a client from Exchange 2008R2 to Exchange 2016.  The way I did it was "the textbook way" I built the new Exchange 2016 server on the same network as the 2008R2 server, and migrated the mailboxes from the old server to the new server, using the migration tool in the ECP interface, then deinstalled the server.  It was a pretty cake migration except for one problem - the internal AD domain name was  "wonkulating.com" however the client had failed to maintain public registration for that domain, and had registered "wonkulatinggronkulator.com" for use on the Internet.   So I set it up so that all internal and external access was to "email address removed for privacy reasons"   User were happy, and the IT dept was able to kick the migration can down the road again.

Well fast forward a decade.  Now I'm an employee for the former client and worse I manage the IT group there - so my can-kicking bandaid has come back to haunt me now that it's time to update to exchange SE.  (it also adds to the fun that there's a couple hundred more users on the network than there were a decade ago)   I decided to cut the Gordion knot and kill off "wonkulating.com" since there's not a snowball's chance in hades we could afford to buy it now.  So I built a new AD for wonkulatinggronkulator.com, and did the jiggery pokery with the DNS servers and setup trust between the forests and so on and now, servers on both domains are happy happy, I can apply both wonkulating.com and wonkulatinggronkulator.com security objects to server filesystems, users can login to either domain at any workstation regardless of what domain the workstation was joined to, and so on, and we are getting ready to migrate the users and workstations off the old AD and on to the new AD.

My question to all of you is this.  I'm planning on installing Exchange SE into the new AD forest wonkulatinggronkulator.com and we will move the users over in groups of 10 or 20 or so, so that staff can make sure everyone is happy, can login, get at their files, etc.  But what I am wondering is if the exchange servers will cooperate with each other.  I'm not using ADMT or any of that to move user objects over to the new server so userIDs will exist in parallel for some time to allow a gradual migration of file and application servers.  (we are too big now for the come-in-on-weekend-and-hose-everything-up-in-a-mad-rush-migration-fueled-with-pizza-and-mountain-dew routine)   It would be very nice to just kick off a migration job on one of the mailservers and have the inbox copied over, but if I have to I can tear out the mailbox on the old server into a PST file and jam it into the new server via import.

Documentation on microsoft.com seems to say at some points the servers will cooperate with each other and at other points it seems to say each mailserver is atomic.  Like most orgs we have a bastion host mailserver that touches the actual Internet, the exchange server is only allowed to provide OWA services to the Internet, while the bastion host server (running Linux, by the way) does the actual heavy lifting of spam scanning and filtering out scam mails.  Only cleaned mail is passed to the on-prem exchange server.   So if the servers -won't- cooperate cross-forest, then I can adjust mail routing on a per-user basis on the bastion host to send incoming mail to the server in wonkulating.com or the server in wonkulatinggronkulator.com depending on which server they are on.

Technically, the ACTUAL user ID on the old AD is WONKULATING\exampleuser while on the new AD it will be WONKULATINGGRONKULATOR\exampleuser, so the servers SHOULD be smart enough to know they are different userIDs - except that the server on wonkulating.com was hacked up by me a decade ago to believe it was authoritative for BOTH "email address removed for privacy reasons" and "email address removed for privacy reasons" email addresses and that they were the same userID basically.  So, I don't know what's going to happen until I try it and all of the documentation I can find on this matter is pretty fluffy, as it assumes you are moving from a domain name you own to a different domain name you own because you bought a company or something, or you are moving from one mailserver to the other inside of the same forest/domain.

Lastly, suggestions to install Exchange SE into wonkulating.com then move it later into wonkulatinggronkulator.com will be /dev/nulled immediately, I'm done kicking the can down the road.  There's more than 20 years of garbage in the wonkulating.com AD and the nonsense described here is just the tip of the iceberg.  (you should see the GPO's in wonkulating.com, simply horrifying)

Thanks!