Would the workstations reuse the former domain profile from the old DC
No, it doesn't work like that. Even though the domain name is the same under the hood it is a new domain. One option here is logon to the new domain once then logon to the pc with another account that has local administrative rights, navigate to
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList
find the new profile and point the Reg_Expand_Sz string named ProfileImagePath to the old domain profile.
and deal with the whole cleanup and migration of services
Not sure what is meant here.
The two prerequisites to introducing the first 2019 or 2022 domain controller are that domain functional level needs to be 2008 or higher and older sysvol FRS replication needs to have been migrated to DFSR
I'd use dcdiag / repadmin tools to verify health correcting all errors found
before starting any
operations. Then stand up the new 2019 or 2022, patch it fully, license it, join existing domain, add active directory domain services, promote it also making it a GC (recommended), transfer FSMO roles over (optional), transfer pdc emulator role (optional), use dcdiag / repadmin tools to again verify health, when all is good you can decommission / demote old one.
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