Beware of how “kommun” is used
At face value, kommun is an easy concept. It refers to a municipality. Sometimes it is translated as local authority. But its use is more complicated than that since it is in many different ways that don’t always translate well.
For example, I’ve come across researchers who refer to a study that covers “all 290 municipalities in Sweden” as a stand in for covering the entire population of Sweden. That is fine if you are familiar with the Swedish context, but for an American reader it would not be evident that this is referring to the entire population. In the US, everyone does not live in a municipality. In Sweden, there is no land and no residents not covered by a municipal administration. In the US, most of the country’s land areas and a large percentage of the population are outside of municipal administrations. Even this can vary from state to state where municipality’s are defined differently.
If you translate kommun as “local government”, an American reader could think you mean the local town administration or even county administration, depending on their context and what they think is more important and regardless of what the facts are.
While I have no single answer to solve this question, be aware of what is really being said by kommun before simply translating it as municipality or local government and think about the reader’s perspective.