I must point that sometimes the "if anything" isn´t so apparent at first. Because sometimes "it is used to suggest or state tentatively that something may be the case (often the opposite of what was just statet).
(idiomatic) Used to suggest or state tentatively that something may be the case (often the opposite of something previously implied).
The situation is, if anything, worsening rather than improving.
Here we could say that the other people previous statement (or what he/she expected to listen was that the situation was improving)
So, it could be replaced by "on the contrary" or "it may not the case" right away (but the answer could be seen as impolite, even arrogant.)
“Do you think she’s tall?” / “Oh, no. If anything, she’s short.”
Oh, no, (here is the clue), it means "on the contrary" or "I don´t think so", but saying that straight away also could be impolite.
“Do you think she’s tall?” / “Oh, yes. If anything, she’s very tall.”
Here´s the "catch", notice that the person doens´t agree with you
, here it´s the equivalent to '"I don´t think so/I wouldn´t agree with you on that one" She´s very tall.
See, in the last one the person is saying "I think you are mistaken/you are mistaken", she isn´t tall. She is very tall.
I found it worthy to bring this up because there is additional and important information. Well, at least to my thinking.