Well there's exit.pub but that's not interoperability so much as a one-way escape hatch. 

 #asknostr
nostr:nevent1qqsgrpyh2qx5jnzmp7883vg958ckwkf267n7j4c5rtpf0syspf83x5qpz3mhxue69uhhyetvv9ujuerpd46hxtnfdupzqk82mqh6zk64qz200a07fqzwpln4kauahmewnvs9z8kv660x6z8eqvzqqqqqqyepa6ph 

 I would immediately mute anyone who did that. The Nostr isn’t a personal backup service for people’s xeets. 

 @rabble has posted and thought a lot on cross-posting, larger fediverse integration I believe 

 Anyone building on xitter to cross-post from nostr? 

 @petri is building a cross posting tool: 
nostr:note1ee09amxhnsmnh6at4t7v8tk6zx4maxkdsywjuq8etm6xm9qsepjqyhs8z4 

 If you post first to Nostr then https://connect.nos.social/ can post it automatically to X.

There’s this that takes the tweet url and posts but it does not have Nostr support: https://github.com/eramdam/tweet-forker

As Fabian mentioned I have been building in this space: www.nootti.com

X API approach is hostile to third parties so it’s not included.
 

 Automatic cross-posting exists between Nostr and Mastodon and it's not great. Technically it works just fine but if you only check the comments and discussions on one platform than it does not create the same experience on the other. 
And even if you were to check comments under both posts you'd be getting the same questions/remarks/jokes twice and a after a while you'd lose interest.