Somehow it doesn't seem that long ago, but the end of mainstream support for Exchange 2016 is actually approaching. From 14.10.2020, Exchange 2016 will be in the extended support phase, which means that there will be no more CUs and only critical security updates and updates for the time zones will be released. The last CU for Exchange 2016 (CU19) will be released in December 2020, after which there will only be security updates until 14.20.2025. CU 18 is expected to be released in September 2020. It is therefore not necessary to migrate to Exchange 2019 immediately just because mainstream support for Exchange 2016 is ending.
On the Exchange Team Blog there is also a statement on the topic of "Management Exchange Server". A "Management Exchange Server" is currently required if the local Active Directory has been synchronized using AADConnect and the mailboxes have been migrated to Microsoft 365. A "Management Exchange Server" is still required for settings and permissions for the migrated mailboxes. The server itself then no longer holds any mailboxes and is only used to manage the settings. The following paragraph on this topic can be found on the Exchange Team Blog:
There is one more consideration for this change that we want to address here today, and that is the ongoing use of Exchange Server 2016 for recipient management for hybrid organizations that have moved all their mailboxes to the cloud.
As you probably also know we have historically provided a free license for these 'management' servers if their only use is to properly manage Exchange attributes when recipient objects are mastered on-premises. You also know that we never provided this free license type for Exchange Server 2019.
We want to assure you that we are still committed to delivering a solution that will allow these lingering servers to be removed, but it will not arrive before Exchange Server 2016 enters Extended Support.Source: Exchange Server 2016 and the End of Mainstream Support
Microsoft is therefore working on a solution to replace the Management Exchange Server. However, the new option will not be ready before the start of Exchange 2016 Extended Support, but will come later. However, as it will be another 5 years before the end of the extended support, you can probably wait patiently until the new solution is ready and do not necessarily have to migrate the Management Exchange Server to Exchange 2019 (migrating Management Exchange Server to Exchange 2019 requires volume licensing).
Anyone running Exchange 2016 in a hybrid or completely on-prem can start thinking about migrating to Exchange 2019 now. There is still enough time, but since Exchange 2019 requires volume licensing and contracts may have to be concluded first, you can start thinking about it now.
By the way: According to Microsoft's Product Lifecycle website, Exchange 2016 and Exchange 2019 have the same end date for Extended Support:
Source: Microsoft Support Lifecycle
Of course, this raises the question of why Exchange 2019 doesn't even get 2 years of extended support instead of the usual 5 years! A lot can still happen between now and then...