Reading the preamble of the treaty is enough because it explains the mindset behind the European project. The Schuman declaration is also short and very clear on the subject. Even though it’s not a treaty or regulation, it’s a clear demonstration that the people at the time saw much further than just the economy. The core message is political integration to prevent Europe from tearing itself apart every 50 years.
I don't think I see free movement of people in Schuman? It's very clear about wanting to move steel and coal but it mentions workers only to suggest that this ECSC should "improve living conditions" for workers. I could squint at this and consider that a steelworker in Duisburg might "improve their living conditions" by retiring to a nice slow-paced village in Southern Italy but just as easily it could mean the ECSC is about workers staying where they are but being able to afford nicer stuff.
However once I'd fought the EU's terrible web search I did sit and read a bunch of the actual Treaty of Rome, and yes that actually does very clearly specify Freedom of Movement for Workers and is broad enough in how it treats this freedom that it's not a surprise courts subsequently concluded that basically every EU citizen should be able to live anywhere in the EU.
