My laptop’s HDD is failing, it shows a bunch of signs such as slow file manipulation and clicking sounds. The Linux btrfs partition keeps going into read-only mode to prevent further damage, makes sense, but the windows partition is working fine (for now).
Shouldn’t harddrive failure be evident on all partitions?
Yup. I would try to stop using it if at all possible. As soon as you can, dump a full disk image to some other storage. Tools like ddrescue can be useful as they will try to re-read failed sectors to get a more complete image.
Once you have the data (or at least as much is available) to a reliable medium then you can start sorting through it and discarding or saving individual bits.
Seconding this. OP, get a new drive, get a live USB with ddrescue on it, and get that transfer started, stat.