How can I manually update offline db with the new osm data change set

You have the wrong file - what you need is not the changeset file but a series of "diffs" from https://planet.openstreetmap.org/replication/ that cover the whole time from when you did the server setup to now.

The manual process is:

• download all files individually
• optionally merge them into a larger file with osmosis or osmium
• copy the individual files or the combined file onto the tile server machine
• apply the individual files or the combined file to your database with osm2pgsql using the exact same command line flags as on the initial import but use the --append flag instead of --create (which is the default)

You could also use osmosis or pyosmium-get-changes to make this easier for you, as these tools have the option of saving their last replication state, so you could let them "download all since last time" and you would not have to go through the hassle of downloading individual files.

Note that updating with diffs only makes sense as long as your data is not older than three or four weeks; once your data is older than that, a full new import is faster than trying diff updates.