A Mac can have, as you know, several Photos Libraries, and this can be very handy. But on any device, there can be only one System Library. It is the System Library that gets synced with iCloud Photos, and it is the System Library that pops up in Mail and other apps when you go to choose pictures from Photos.
As muguy says, your Libraries remain separate-- and merging them takes extra work, so it will not happen without you forcing it to happen.
If you want to make sure about the System Library, there are two ways to check. You can look at Photos>Settings>General, like this:

The choice "Use as System Photo Library" is grayed out, because this Library is already designated the System Library. If somehow your Libraries get mixed up, be sure to click this on the one you want to sync with iCloud. Only when this Library is the System Library can it be connected to iCloud.
You can also close Photos and option-click on the Photos icon to bring up this dialog:

which shows all your Libraries and tells which one is the System Library.
If you use the Migration Assistant to start your new Mac, this should all be automatic.