eas build fail - showing "Cannot read properties of null (reading 'children')"

Are you using this? You don’t have react-dom or react-native-web, so maybe not unless maybe you’re bundling some stuff to load in a webview? If you’re not using it you might want to remove it. It should of course not be causing problems, but generally best to remove things you don’t need. Also, if you do need it it really belongs in devDependencies rather than dependencies.

But that’s not the cause of the problem.

If I try this with your deps it works for me. I was using yarn instead of npm, though.
Then I removed yarn.lock and ran npm install. That gave me the same error. I checked npm’s debug log and that pointed me at this part of npm’s code:

      // First, see if it's ok to just replace the peerSet entirely.
      // we do this by walking out from the entryEdge, because in a case like
      // this:
      //
      // v -> PEER(a@1||2)
      // a@1 -> PEER(b@1)
      // a@2 -> PEER(b@2)
      // b@1 -> PEER(a@1)
      // b@2 -> PEER(a@2)
      //
      // root
      // +-- v
      // +-- a@2
      // +-- b@2
      //
      // Trying to place a peer group of (a@1, b@1) would fail to note that
      // they can be replaced, if we did it by looping 1 by 1.  If we are
      // replacing something, we don't have to check its peer deps, because
      // the peerDeps in the placed peerSet will presumably satisfy.
      const entryNode = entryEdge.to
      const entryRep = dep.parent.children.get(entryNode.name)
      if (entryRep) {
        if (entryRep.canReplace(entryNode, dep.parent.children.keys())) {
          continue
        }
      }

in particular, this line:

      const entryRep = dep.parent.children.get(entryNode.name)

Since this seems to have something to do with peer dependencies I tried running it with the --legacy-peer-deps option in case it helped, and indeed it did!

So it seems there’s something dodgy going on with the peer dependencies of one or more of the packages you have installed, and in addition there’s a possible npm bug.

As a workaround, you could ensure that npm install runs with the legacy-peer-deps option set to true: