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.
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.

In the past seasons, how the format use to be before now, this is the time the long break is always given and the final stage of 16 usually begins in February. But since we have many matches to be played now and the time allocated for them couple with International breaks too, they had to adjust somethings. When this first round of the competition is over, we may not see a long break between this first round and the round of 16’s, it’s going to be a back to back kind of entertainment. Will be anticipating for the next round to kick off by January 21st, I want to see the fate of this three teams you’ve mentioned.
Their experience is one thing they keep leveraging on and never letting any situation at any time be a reason to back out or fall back in their pursuit and change for the league title, even when every other person be thinking or seeing that they may not be able to win, they still stay very optimistic and resilient in their chase and most often they get the best rewards off it so seeing and hearing this from ancelotti isn't like a surprise and he always believes he's got his shit together and Indeed he does.
I also have not giving up on Real Madrid yet in the champions league. They always come out victorious all the time, despite the difficulties they face in the league title. The La Liga is very much one part that they won’t joke with and they’re already dominating there even though they started poorly. The champions league is one of their major competitions they never joke with, so I’m still expecting a performance from them that will see them through to the round of 16. Champions league is going to be very intriguing as usual and Real Madrid could still be a major contender.