While I agree with the answers from a literal interpretation, I think it's helpful to understand that this phrase is idiomatic in usage and understanding. I initially said 'nearly idiomatic' because (for native English speakers, at least) the literal meaning is so near to the idiomatic meaning that it's hard to even realize it is idiomatic. The context is basically always that a solution is intended to improve a situation and the speaker (or writer) is claiming is actually going to make the problem worse. It really isn't important whether the solution actually does any specific good, it's that the overall result is bad.
The reason you would use this phrase instead of "harm rather than good" is:
To acknowledge that the solution is based on good intentions.
To acknowledge that there may be some benefits to the solution.
But mainly it's about 1. Basically: a way to soften criticism of a solution within a debate or discussion. If you simply said, "your solution does harm", it can come across as an attack on the originators or supporters of that solution. The use of this phrase implies that intentions behind the solution are good even if the result is bad.
You write in your addendum:
These are all in line with the definition of the Oxford dictionary in that the expression isn't about a quantitative comparison of harm and good. So those who argue that the expression is about such a comparison should provide some authoritative source.
I think you are a little confused about this in general. The reason these sources don't refer to the literal meaning of the words is that this is an idiomatic expression as listed in Merriam-Webster.
An idiom is a phrase or an expression that has a figurative, or sometimes literal, meaning. Categorized as formulaic language, an idiom's figurative meaning is different from the literal meaning.
That's why there's an entry for the phrase is the first place. If you search for other phrases on the the Lexico (Oxford) site you've linked to, you won't find any grammatically correct phrase you type. It's only those phrases that have some other connotation apart from what the literal words say.
You cannot be fluent in English without becoming familiar with common idioms. From the wikipedia article above: "In the English language alone, it is estimated that there are at least twenty-five thousand idiomatic expressions." Most native English speakers use so many idioms in their speech and writing that they are not even aware they are idiomatic.
The phrase makes sense literally but that's not the what the idiom means. For example, if I say someone is "high as a kite" it has a literal meaning: 'positioned at an altitude where a kite would fly' but that's not what it means. It means the person is intoxicated.
So trying to figure out how to 'parse' this semantically to come to the definitions you are finding doesn't make sense. Those definitions are for the phrase as an idiom, not what the words mean semantically.