should I lift them off the paper after soaking or should I leave these the way they are ?
The more you mess with stamps, the more damaged they become.
If you have a prospectus on how you intend to collect stamps, henceforth,
say a stamp album, Steiner Pages, Stamp Mounts etc,
Then certainly remove and relocate.
Removing and putting in a box, envelopes etc, then I would leave as is,
until your regime is determined.
Indian stamps come in the billions, can be an enjoyable pursuit.