spoliers~ please read on your own discretion as I will explain FULLY by full I mean FULL.
In the webtoon, it was shown that Sung Hyunjae seems to be sensitive about the regression (such as imagining Han Yoojin's face to be older~ stuff like that).
Sung Hyunjae at the time felt like preparing and just the birthday party was something he had already experienced (which he did), hence the bad mood he's been having. Because he felt so bored of doing the same thing again.
I guess this explaination will be shown more probably the next chapter, such as Bak Yerim's invitation being late (Since she was just an A rank in the first timeline) and Myungwoo's being even later (since he was presumably dead/just a simple f rank).
Han Yoojin wasn't invited because Sung Hyunjae felt a sense of dissonance, and he was probably gonna exclude Han Yoojin and compare what he was feeling (Han Yoojin's thoughts in the webnovel)
another simple explaination is because Han Yoojin doesn't really need a invite because you know. he is sung Hyunjae's beloved.... Item! ╮(￣▽￣)╭
Remove the item because we all know dada( ° ʖ °)
But Yoojin will come in the end right? But how he do that without invitation?
Yes he will lolol. As for how he did that, without spoilers it's basically just my 2nd comment. But for spoilers.....
Basically Yoojin visits Sung Hyunjae, after having a convo where Sung Hyunjae affirms that "since your my item, you don't need an invite" Han Yoojin joins those who were invited on their way to the birthday party. And since Song Taewon was the one checking, obviously both stw and hyj know that sung Hyunjae giving no invite doesn't matter lol
Why he being sweet here by saying that lol XD
Like you're my lover, why I need to invite you XD
I mean technically they are lovers... Cough cough cough who said that??
Whoever said it, they were right
Ahh so rn in the last panel, he is still himself (thinking that hyj is his item= no need to invite) but also feeling disconnected to the timeline?
the btch is just spouting crap so his item aka omega aka wife wont get mad.
THANK YOU FOR YOUE SERVICE so hes not the self aware from the other timeline Hyunjae. It was just a sense of dejavu (not). i was legit panicking because i cannot handle anymore misunderstanding arc this season
GUYS I NEED SOMEONE WHO CAN TELL ME WHY HE DID NOT GOVE YOOJIN AN INVITATION