The point of reusable bags is not to save the miniscule amount of energy it takes to make a plastic bag. It's to keep plastic bags out of the waste stream where they end up clogging rivers and take thousands of years to decompose.
I'm pretty confident that it's minuscule locally (these aren't European rivers: https://www.google.com/search?q=plastic+waste+river&tbm=isch), but I couldn't find solid data on waste that gets first exported, then dumped into a river.
Say it takes 1 year (probably less) from when a bag is created to when it gets thrown away. After it gets thrown away, it takes 100-1000 years to completely decompose. That means bags are entering the landfill faster than they are "leaving" via decomposition. That's going to be a problem. After enough time we'd just be like a malicious or poorly-designed AI that covered the Earth in plastic bags rather than paper clips.
Supposing for the sake of the argument you're right, that means we need enough landfill space for 500 years' worth of plastic bags. Is that really so much space that it's a problem?
I've also been to countries where these bags make it into the ocean and become micro plastics. As with all things there are pros and cons. Most of our civilization has cons for the environment, but from what I can tell the best situation for most people who's garbage makes it to a landfill is to use mult-reuse recycled plastic bags.
Being as I've already made the commitment to the cloth bags I just have to keep using them until they hit their 131st use, then keep going.
Since Australia banned single use plastic bags at supermarkets I have not seen a single bag floating around the street which used to be a common sight.
They get washed once in a while when they inevitably get dirty and I can repair them quite easily if a stitch finally fails or they get tears, which hasn't happened yet.
People need to keep and use what they already have instead of lazily buying more new stuff all the time.