It seems like it should be a classic garden path sentence: you get to the end, fourteen words later, and realize that 'anything' wasn't the subject of 'has' and the 'then'-clause you were expecting isn't going to appear.
However, in practice it reads okay without marking off 'if anything'. This must be such a common expression that we automatically read it correctly even when unmarked by commas. Which surprises me.
The objection to putting two commas around it is the previous comma: you then have three in quick succession, which looks choppy. In this situation I prefer to drop the two surrounding commas if possible.
The difference in pronunciation is subtle. If 'anything' is subject of 'has', it's all said at level pitch until a main accent later on (which could come in various places, but the primary possibility is 'Web'); but if 'if anything' is an adjunct, and 'has' has no subject, then 'if anything' is probably spoken with rising tone (without commas) or fall-rise (with commas).