Freelancing is a spectrum. The one end is mostly anonymous on the web - there are four hundred web designers and the customer picks one mostly at random. As has been observed this is a very competitive global industry. It typically involves very well defined objectives (though I'm sure the freelancer will say otherwise

) from the customer - they're just paying for a commodity product
The other one, the one I think you want to be in, is more personal and requires expertise. I have a problem I can't solve, I ask around and find out Zap is the only one who knows how to do it in America. Yeah someone in China can also solve it, but how am I supposed to figure out which person? The problem is important and I want the right solution to it, so I hire an expert and I pay them like an expert. This probably looks a bit more like consulting to be honest, you're not just paying them to do well defined labor, you're paying them to figure out what labor should be done.
I believe I could offer services for ad hoc business process automation, or automating messy manual data processing tasks that no one wants to do.
This sounds closer to the latter than the former. Mostly no one who understands what should be automated is not already automating it. Your target customer feels like owners of small businesses with no or only a couple employees, and not much programming experience. They probably don't even know that they could save money automating things. The value added you would bring is not writing some vba code to automate an excel spreadsheet they haven't changed in ten years, it's knowing that you can even write that vba and it will save a bunch of time. They aren't going to ask some random person on Fivrr for help, what they need is for someone to come to the office and spend the day watching what they do to see what can be improved.
Sounds like a fun job actually, but I'm not sure how you get it. Certainly if you had a couple happy customers word of mouth would get around, but getting the first references seems tough.
I also could be wrong, I don't actually do work like that and maybe less of it exists than we are imagining.