There's a lot of talk about manganese recently in relation to joints. Although there isn't a great deal of evidence to support it's use to help arthritis there is some. When it comes to relieving symptoms such as pain and stiffness. There have been a couple of clinical studies that show it can slightly improve the effectiveness of Glucosamineand Chondroitin,  but there are equally as many that have shown it makes no difference at all. 
The working theory for why it may work, is that it can increase something known as an SOD level. That's how many anti oxidants are in your blood stream. Which in theory could lead to reduced inflammation.
In short there's some evidence to suggest it could have some use in a combined joint supplement, but probably not much use on its own. As such we wouldn't recommend it as a go to dietary supplement for arthritis, but it has place in an overall health regimen. It is worth noting however, manganese plays a vital role in bone formation, brain function, and the activation of various enzymes in the body so it is important to make sure you have enough.
It does seem to have a bit more of an impact on bones though so could be useful for other conditions which still effect the joints, but are related more to bone issues.
But, over supplementing, won't do much.
The Often Cited RA Study Of Manganese
One study found that individuals with rheumatoid arthritis had higher levels of manganese in their granulocytes, a type of white blood cell involved in the inflammatory process. This suggests that manganese may play a role in managing inflammation associated with arthritis, but we still don't know much more than that.
What Else Can I Use Manganese For?
Studies have shown that individuals with weak bones who took a supplement containing manganese, along with other nutrients like vitamin D and magnesium, experienced improvements in bone mass. 
It's An Anti Oxidant
Manganese is a part of the antioxidant enzyme called superoxide dismutase (SOD), which helps protect against free radicals in the body. Free radicals are molecules that can cause damage to cells and contribute to aging, heart disease, and certain types of cancer. SOD helps convert these harmful free radicals into less damaging molecules. And yes we know anti oxidants can have some positive impact on the joints, but again we're not saying manganese is bad. Just not overly useful. 
Manganese and Blood Sugar
Manganese may also play a role in regulating blood sugar levels. Research has shown that individuals with diabetes have lower manganese blood levels compared to those without the condition. 
Manganese Side Effects
For adults aged 19 and older, the recommended daily intake of manganese is 2.3 mg for males and 1.8 mg for females. It is generally safe to consume up to 11 mg of manganese daily. However, taking excessive amounts of manganese can lead to adverse effects, such as Parkinson's disease-like symptoms. Individuals with liver or kidney disease should exercise caution when consuming manganese, as their bodies may have difficulty eliminating excess amounts.
Is Manganese Good For Arthritis?
Manganese is an essential mineral that plays a crucial role in various bodily functions, including bone health, inflammation regulation, and blood sugar control. Ultimately however it's not really a supplement we'd recommend for arthritis, sure it's good for bone health, which isn't going to do any harm, but there's dozens of other joint supplements that could have a greater impact than manganese.
1 - https://pubmed.ncbi.nlm.nih.gov/10050562/
2 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3392795/
3 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9586363/
4 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5844859/
5 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3973834/