Here are detailed information about the limitation for Exchange online mailbox, have a check about it:
For more detailed information, you can have a look about this article: Exchange Online limits
Yes, on Exchange 2010, there can only exist one Public Folder Database. For Exchange 2013 and later, Public folder is hosted on Public Folder Mailbox rather than Public Folder Database. You could create more than one Public Folder Mailbox.
If your Public Folder beyond the limitation, I would suggest you backup part of them, then delete them from Public Folder. After migration Public folder to Exchange online, recreate those folders and import data to it.
You can also migrate Public Folder to Exchange 2016 first, then migrate to Exchange online. In this way, you will have a newer Exchange on-premises server to manage mailboxes(In a hybrid mode, you need to manage migrated mailboxes from Exchange on-premises).
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