I’ve worked in the water industry on the wastewater side for many years. Most smaller rural sewage works with biological trickling filters don’t usually smell too bad. However, some filter works have big issues with huge amounts of very tiny flies – this is a difficult and expensive problem for the water company to deal with. Sometimes you’d visit site, get out/in your car and literally dozens of flies would find their way in. Sites with trees seem to have worse problems.
There will be various bit of equipment such as recirculation pumps that will automatically operating 24 hours so depending on how close you are mechanical noise could be noticeable. Sludge will need to be removed by road tanker on a regular basis which can generate smell issues and vehicle noise. In the event of operational problems or a sewage works extension, there is potential for lots of vehicle movement and temporary pumping/standby generators which can also cause disruption.
A small well run plant is unlikely to be a problem but that said I wouldn’t want to live next to one!