The real answers here should be in the data, but as an anecdote I experienced something that genuinely impressed me the other day.
I’m in the market for a new mattress, and the other day on a whim I stopped at a mattress store (in real life). After I left the store, within an hour, I looked at a site I commonly look at (a political site), and saw a banner ad for the mattress store company.
In any case, it’s hard for me to believe that targeted advertising doesn’t work, because without it, I see adds in product categories I will never buy in.