What does that mean? When you post, who’s server’s outbox do you post from? Inboxes and outboxes by server are a central part of the standard.

The server my account is stored on.

or any other, I don't give a shit, I'm not sure why this would make a difference, but that seems like the obvious answer to me.

You can copy over a user, and make another similar account (like pixelfed), or you can do stuff on that server from another federated server, but at the end of the day you’re not on the same account on different servers.

I don't know why the current pixelfed app needs to make a separate account.

I gather it finds that solution most convenient, as it means the fewest interactions with the Mastodon server, and there's currently no straightforward for the current pixelfed app to establish a secure long-term session with a non-pixelfed server. I understand that it currently does make a separate account.

I don't understand why it is inconceivable for the activitypub protocol to support such communication. eMail has multiple standards that let me log into Thunderbird from non-Thunderbird email servers.

Sure. It’d be a pretty huge departure, though. To a weird degree, like Coca-Cola leaving the beverage business becoming a tire company.

If you wanted to make a new protocol, you could go beyond federation and have a fully decentralised system where everything happens on arbitrarily many servers in parallel, but that would be a lot of work and probably data-heavy before any users walk through the door.

I feel like you're describing something I'm not calling for. I'm not calling for accounts to be mirrored to multiple servers. I'm calling for a system where client applications can access different servers without copying accounts to a more familiar server.