I don't have an ableton system, so I cannot test on my devices.
If the file were too large or incompatible, GarageBand would have refused to load it. But your music may be to complex to be played in real time - to many articulations, for example. You could test this by muting most tracks but your new vocals and just one or the Ableton tracks and see, if the result is better.
Restart the Mac and do not start any other app but GarageBand. Make sure, your GarageBand project is on the internal drive, not on a slow, external drive.
Perhaps this help page by Ableton can help: https://help.ableton.com/hc/en-us/articles/209072289-How-to-reduce-latency
DO you have any effects applied on the problematic vocal track, that could change the timing? Look in the Editor for the vocal region for the selected region, if the quantization is enabled, or "follow tempo and Pitch". This could change the tempo or the quantization.
Sorry, I cannot change the labguage right now from German to English, but I hope the screenshot can tell you where to look: 