If I’m not free to join the Fediverse from the server of my choice, whether that’s mastodon.social or threads.net, is the Fediverse truly free?

Joining the fediverse is just a matter of using a platform that implements ActivityPub (the protocol that lets servers communicate with each other. If Threads implements ActivityPub, it's part of the fediverse, and the people on Threads can interact without any instance that chooses to federate.

However, instances don't have to federate with Threads. That's part of the freedom of the fediverse. If an instance admin decides that they don't want to deal with an influx of hate, don't want most of the content their uses see to be from Meta, or just don't want to federate with a for-profit company that has an awful track record, they should be able to defederate. If a user of that instance really wants to see Threads content, they should be able to move to an instance that lets them, but defederation doesn't make the fediverse or ActivityPub less free.