Tool to migrate Public folder from Multi Forest AD to office 365 with different root folder

Yes - both BT Migrator Pro for Exchange and Migration Manager for Exchange can help here (flexible mapping of PF hierarchies from multiple sources). Best check with a sales rep (and presales specialist) for details.

https://www.binarytree.com/products/binary-tree-migrator-pro-for-exchange/

Seems BT Migrator Pro is for 2007/2010 to EXO and not for EX 2016 to EXO.  I already raise the concern with sales rep and awaiting reply, if you got any input then do let us know.

Please ... just because out development is much faster than our marketing ... ^^
"Source: Exchange Server 2010, 2013, 2016, or 2019
Target: Exchange Server 2013, 2016, or 2019 or Office 365"
datasheet-binary-tree-migrator-pro-by-quest-for-exchange-datasheet-145711.pdf (binarytree.com)
Binary Tree Migrator Pro for Exchange 20.10.1 - Release Notes (quest.com)
Binary Tree Migrator Pro for Exchange 20.10.1 - Requirements (quest.com)

Please ... just because out development is much faster than our marketing ... ^^
"Source: Exchange Server 2010, 2013, 2016, or 2019
Target: Exchange Server 2013, 2016, or 2019 or Office 365"
datasheet-binary-tree-migrator-pro-by-quest-for-exchange-datasheet-145711.pdf (binarytree.com)
Binary Tree Migrator Pro for Exchange 20.10.1 - Release Notes (quest.com)
Binary Tree Migrator Pro for Exchange 20.10.1 - Requirements (quest.com)