While there's plenty I like about the series, I've got to say that the Christmas Special is something of a low point. Not that I'm a party pooper, but I don't feel that the songs in the Christmas episode are a good fit.
Songs in a TV series can work - just look at Phineas and Ferb. But here they seem forced and rushed. I'm sure they probably worked better in the original French dub, but in English the word "me" is rhymed with itself (possibly on more than 1 occiasion) and the voice actors sound like they're struggling to keep up. Maybe with a few more takes they would have sounded better.
But the worst offender is Santa Claws who repeats his short song at least 3 times in succession without any significant changes. We heard you the first time!
Other than that, the episode was a nice change of pace and it was interesting to see Gabriel's reaction to pretty much the entire cast showing up at his house at the end.
Sorry to hear you didn't enjoy the Christmas special. Personally, I actually really liked it! After "Volpina", I'd rank it as my second favorite episode. For me, it stood out from the other episodes by focusing on genuine character moments rather than simply having a somewhat forced intro and then jumping right to the villain, as a lot of the other episodes have done.
I'm not sure I ever watched the English dub all the way through, but from what I've seen I actually agree with your assessment of the songs. But in the French dub I only really had a problem with the first song…it seemed quite rushed and it didn't really seem like there was a particular point to it. But I liked all the other songs. "Cat in the Night", "The Boy That I Secretly Love", and "We All Have the Right" all involved important character moments, and I thought the instrumentals were very good, as were the French lyrics. And I liked "Bad Santa Claws" because I thought it was hilarious, and I thought the completely unnecessary repetition made it even better.
I'd recommend watching it in French if you can! I'm actually not really a fan of the English dub in general; for every episode I think both the script and the voice acting are better in the French dub.
Both on the French and English version of the Christmas Special, I admit I have mixed feelings about it and the songs overall. I don't think the songs were necessary, as the 22-minute run time made them feel rushed, and most of them didn't feel like they were connecting well to the story. If the special had been double-length like originally conceived, I think the songs' quality would have been better and wouldn't have felt as much like they were hindering the plot in some ways. Just in the show itself, it felt unnatural for there to be a musical episode in-universe. It makes sense in Phineas and Ferb, who break into song all the time throughout multiple episodes, but it felt like an odd genre shift for Miraculous for just one episode.
However, while I'm not a huge fan of the songs, I do like them, and I think the crew did a good job as best as they could with the short amount of time they had to make this special. "Cat in the Night" and "The Boy That I Secretly Love" were nice and decent looks into characters' feelings, and I thought "Bad Santa Claws" was joyfully silly. The singers did a good job too. The French voice actors and the majority of the English voice actors sound really good. The notable exception would be Bryce Papenbrook, Adrien's English voice actor who has stated multiple times he is not a singer, but for doing something uncomfortable to him, he did an okay job that I can't be upset at him for.
Story-wise, it definitely could've been better, but I like the ideas they had within it, and most of those ideas well excuted not too badly. It was nice to see Adrien's family dynamic and struggles with missing his mother and feeling ignored by his father, and the same goes for Gabriel with his struggles to move on from his wife's disappearance and express love to his son. The akumatization cause was a bit forced and strange, but not hard to believe happening, and it was nice to see Adrien bond with a kindly older man. I wish there had been more purpose given to Marinette in this episode, but for the sake of time, it couldn't be, and a wiser choice was made to focus a bit more on Adrien's struggles, something we usually get less often in regular episodes.
In the end, I mostly agree that I don't think the songs were a good choice in the end for the special, and I'm honestly not eager for another full-on musical episode if we ever get another one, which we have heard may happen. As long as it makes sense in-unverse, I can at least forgive it, however, like if there's a musical stage production being done by Marinette's class or there's a music competition. With more time, a better fleshed-out story, and a longer running time, the crew would've probably ended up with making better songs that work well with the context and plot of the episode, but I can forgive them in this case for coming out with fine enough songs because they didn't have those options available.
I really enjoyed this episode along with the songs. It's true that the French dub singing was better, but Cristina Vee has a beautiful voice. As I also mentioned in the comments, Bryce Papenbrook has a good voice but not a great one and as someone said earlier here, has repeatedly said that he's not a singer. But he does have a really good voice for calm, peaceful songs, like "Brand New Day" and "We All Have The Right." I actually found myself replaying them; they're cool.
And as for "The Boy That I Secretly Love," I loved it. I still agree that her French voice is better, however. I found it on accident. Before I actually watched the episode, I watched a video with all the songs, which were in French. All I knew when I started watching it was "Cat in the Night." But then the video kept playing and I totally freaked out (on the positive side) when Ladybug started singing. As an opinion, I consider her voice to be the prettiest female French singing ever... Anyway, the video had no subtitles, and when I finally found one that did (with The English dub still not out) I freaked again and was romantic-fangirling the entire time while writing down the lyrics. lol
I don't really know what I think of Santa Claws's singing, actually. This time, I have to say his English voice actor is a better singer. His French one really wasn't too good, and his dancing... Wow. Just wow. He dabbed. Santa Claws dabbed. I laughed so hard... XD
Plagg isn't really a singer either. Especially since his voice actor puts on a voice for him. But at least he was on tune, right? ;)
Cat Noir's second piece was awesome. Still better in the French, but English was good too. Plus, as Lilanette brought up in the comments, the soundtracks (in the backround, not the songs they sing) were almost entirely new. And beautiful. I have never wished more that the creators would release YouTube videos with just those pieces, and no words.
So yeah, there's my opinion: I absolutely loved it. My only disappointment was that it didn't turn out to be forty minutes long.