> That's only possible if you sacrifice some of the stronger anonymity requirements

Untrue. You can use strong encryption to ensure confidentiality and zero-knowledge proofs to ensure integrity. Then, you can use methods from homomorphic encryption to tally the ballots. There is a whole area of research dedicated to this.

So in your opinion the problem is (theoretically) solved? As in, we can have anonymous, verifiable, online, direct democracy such that 3rd parties cannot verify your vote without your private key?

As I said in another comment, individual verifiability and non-coercion are mutually exclusive online. However, there are indeed solutions for the other properties (including global integrity), and compromises between individual verifiability and non-coercion. For instance, you can have a look at Helios [1] or Belenios [2]. Current research is looking for stronger guarantees, a better compromise, or a more interesting voting system (such as Single Transferable Vote or Majority Judgment).

[1] https://vote.heliosvoting.org/

[2] http://www.belenios.org/