Denmark (Copenhagen) to Netherlands (Amsterdam)

Hi! 

I’m travelling solo this summer throughout Europe, and this is my first time using eurail! 

I bought a 22 days pass so I’m hoping to travel by train as much as possible (in terms of travelling between cities/ countries) and not resort to other transport such as plane/ bus etc.. 

I need to go from Copenhagen to Amsterdam (or Utrecht) on 27 July, which requires me to first take a train to Hamburg 

I saw on the DB website (https://reiseauskunft.bahn.de/bin/query.exe/en?ld=43108&protocol=https:&seqnr=1&ident=2s.08833108.1685120803&rt=1&OK#hfsseq2|2s.08833108.1685120803) that I can go by a direct night train EN345 which operates on 27 July 2023 and is operated by SJ and reservation is compulsory 

I then went to SJ’s website (https://www.sj.se/en/kop-resa/valj-resa/K%C3%B6benhavn%20H/Hamburg%20Hbf/2023-07-27) to make a reservation but couldn’t find EN345 here nor any trains by SJ from Copenhagen to Hamberg that allows me to reserve any trains 

Now I have these questions: 

1. Have I used the wrong method to find trains that’s covered by my eurail pass? 
2. Are there any other ways to go from Copenhagen to Hamburg/ Amsterdam by trains covered by eurail pass?

I’d highly appreciate any help! Thank you!