I'm Singaporean myself and have been following the local league quite religiously. Also have been mainly playing long term saves on the Singapore league on FM for the past few editions.
The Young Lions are placed in the league in hopes to get younger players more regular game time to develop. But irl this hasn't really worked out, with the team regularly finishing near the bottom of the league. The best players do get poached, while the team has little consistency because majority of the players are serving their military service, and may not have full availability, and most return to the other clubs after they are done with their service. Military service isn't replicated in the game like the South Korean league in the game, so in some sense you have greater control over in/outs in the SPL in the game.
I know the above doesn't explain why they don't qualify continentally, but the rule has been there ever since the team was added to the league 20 years back. But perhaps it's just the premise that they're a developmental side and hence have no place in representing the country at club continental competitions.
Young Lions are participating in the cup this year irl (which is ongoing right now btw), but it's been pretty inconsistent regarding their presence in the cup, almost as if they were there to make up the numbers at times. The last they they did was 2016, so I think it's understandable that the game hasn't coded them in this year, as we haven't had the cup for two years due to covid, and the cup draw for this year was only made around August or September.