I'm curious about why there is such a big time gap between Round 6 and Round 7.

Next games are starting by January 21. I don't remember such a big interval during the group stage in the old format honestly. This kind of a break was only given during the time between the end of the group stage and last 16 phase. I miss the games already.
For us as spectators or football fans, of course such a long break is very annoying. But for the team and coach, of course this long break is very good, even with this new format, aren't many coaches complaining about the tight schedule?
But whatever the reason for this long break, of course it's because it's the end of the year and it's already the holiday season. This may be the policy of all parties, except for the EPL which doesn't recognize holidays.
The points are still really close in most parts of the standings. Balances can change very easily to determine top 8 qualifiers and teams joining playoffs. I'm wondering what Real Madrid, Manchester City and especially PSG will do.

Yes, everyone must be curious about the teams that will qualify for the last 16 or the teams that qualify for the play-offs. Moreover, there are big teams that are even favorites but are still not safe in the remaining two matches. However, if you look at the current performance improvement, I predict that Real Madrid will qualify with PSG, while Man City will fail to advance to the next round because their confidence has decreased, both coaches and players, just look at them continuing to lose and that will definitely have an impact on the remaining two matches, especially since they will also face a tough match against PSG.