We are currently researching how to move/migrate Sharepoint 2013 On-Premises to Sharepoint Online, and based on what I found, Microsoft has a solution named SPMT. However, based on some answers I read, it only supports migrating files and document libraries. I'm looking to move the entire site (including site pages structure and web parts), is there any OOB solution for this or if there isn't, which 3rd party tool would you recommend? Thanks before!
I've never used Microsoft's tool, but we did our entire SP2010 to SPO migration using Metalogix Essentials (from Quest Software). There is a ton of customization on what you'd like to migrate to SPO like navigation, home page, item level permissions, etc.
You can do the free trial and see if it would meet your needs. My company had already purchased it prior to me joining the organization, but I was happy with the software and how it worked.
I suggest that you use ShareGate to migrate site pages and web parts from on-premise to online.