How should I write literature review for a paper that is an extension of my own research paper?
I think the best approach is to think of them as two completely separate papers. When you write the second paper you should write it as if you have read but not authored the first. You therefore need to add the necessary background and literature review to make it stand on its own. The reason for this is that anyone who finds your (second) paper once published will not necessarily know of the connection, may not have read the first, and will need a reasonable introduction to the subject.

So, each paper should be an entity of its own. The only clear case where this may not be necessary is if you publish two papers back to back as part 1 and 2 of a series with the same main title but differing sub-titles. Then it is clear that the papers belong together and you may expect people to note and read both papers to a larger extent.