I have this weird problem where I can consistently hear the note and sing extremely in tune in a group setting, with the artist also singing in the background of a track, or even while I'm playing the backtracking on guitar, piano, or ukulele, but for some reason I struggle to sing in tune solo with like a karaoke track. Is there any reason for this, Is it normal? And is there any way to fix this?
That is a common problem and it's perfectly normal. Many folks can only sing karaoke with the guide vocals in the mix. I don't use backing tracks when I perform mainly because I don't have time to practice with the specific backing track to get my timing synchronized perfectly with the track.
When you hear the singer on the recording you can simply sing along with the singer listening to the vocals on the track for not only the correct pitch but also timing of the vocals as they relate to the musical arrangement.
When you play an instrument, you are creating your own timing as far as how the vocals relate to what you are playing on your instrument. You can deviate from the recording when you play the music yourself. But you can't deviate from the musical arrangement that was created to go with the specific vocal line it goes with.
When you try to sing to a karaoke track containing music but no reference vocals, it is easy to get out of sync with the musical arrangement. If you get just a beat behind (or ahead), you will be hearing the wrong notes for the part you are singing or be ahead of or behind the chord changes with your vocal. It's easier when the karaoke has the words synchronized with the music but it is never perfectly synchronized.
You stated that you are able to sing in tune (in key) when the vocals are present or while playing an instrument to provide your own accompaniment. So hitting the note that corresponds to what you hear is not the problem. When your timing is even a tiny bit off, your brain knows what note you think the vocals should be singing but that is not corresponding to what you are hearing in the music and your brain gets confused and tries to make adjustments. If you sing the correct note but at the wrong time to correspond to the music, it will not seem right.
What you need to do is listen to the musical arrangement with the vocals that go with that particular arrangement over and over again and dissect the music in great detail to see how aspects of the musical arrangement relate to the timing of the vocal arrangement.
You must find certain ques in the music as a reference point for the timing of the vocal line. For example there might be a riff on a sax right before the bridge starts or a particular drum pattern that is played leading into the chorus.
Before singing along, listen to the entire track several times making mental notes of how the lyrics relate to what is going on musically. Then start singing along and try to stay right on top of the vocals with your timing.
After you are able to sync the timing of your vocals with what is on the recording, start singing along to the karaoke track with vocals removed. Take it in small sections. Master singing the first verse before you try the chorus. Then take the chorus in isolation until you have it down. Then put the verse and chorus together. Same for the bridge if there is one.
Once you can sing the song to the karaoke arrangement almost exactly like the original singer, you can play around with your own personal embellishments or variations if you like. But the timing can't be changed when singing to a pre-recorded track.
It takes practice, practice practice. That's all. The good news is that the process of dissecting the musical arrangement will improve your skill as a musician.
Good luck and have fun!