In my country, single use plastic bags were replaced with thicker reusable plastic bags that many people discard after a single use. So the total volume of produced/discarded plastic probably increased despite the number of bags used probably going down. I don't have sources other than anecdotal evidence based on behaviours I observe.
if your goal is to eliminate plastic, or fossil fuel emissions, I'm not convinced these bans have been effective.
Plastic bag bans have been sufficiently successful that people have forgotten this was a problem.
Edit: Apparently this is commissioned by the plastic industry. It does match my anecdata of how many people I see buying "reusable" bags at the supermarket check out, combined with https://ourworldindata.org/grapher/grocery-bag-environmental...
What country?