First of all there is a track work that weekend so trains need to do a detour (if they run at all).
On SJ you can usually see a disabled option for trains during track works until SJ has decided the details, like the night train Malmö-Stockholm on June 12. So a bit worrying that nothing shows up on June 13. In the yearly timetable from the transport administration SJ has permit for two trains Malmö-Stockholm (taking around 6.5 hours from Malmö) and they usually always run some trains during track works so I think there is a big chance for SJ trains but there is no guarantee.
Second problem is that trains start in Malmö and you need to connect with Öresundståg Copenhagen-Malmö. Going in the Copenhagen-Stockholm direction it's highly recommended to have both trips on one ticket. Öresundståg has been a bit late with ticket release this year but now I see that they've released until June 8th which is almost three months so better now. It still explains why you see strange options for June 13th, with no commuter trains released you will only see a few buses between Denmark and Sweden.
Snälltåget is a competitor, they allow two pieces of luggage of 55 x 45 x 25 cm (21.65 x 17.72 x 9.84 inches) so basically a large airline cabin luggage. In reality larges sizes probably work but still they have the right to refuse travel with larger luggage. With larger luggage it would be too risky for me.
If you want to travel by train despite the detour, you should wait a bit to see what SJ is doing. The night train on 12th is probably a good indicator, tickets for that and any possible tickets for 13th are probably released more or less at the same time.
I see track works Stockholm-Oslo the weekend after, when do you plan to travel?
