What advice do you have for managing a situation where my soldier has been arrested following his involvement in a fight at a local bar?

prosecution in the local court is about 100% likely
And frankly you have zero responsibility to do anything about it for it or support it.
Other than keep the chain of command informed on his court dates and the outcome.
As well as process his leave form to give him time to go to court because I sure as heck wouldn’t give him free time off

My mother had a saying I remember it to this day and have used it widely over my 56 years.
“Self-imposed pain gets no pity “

What SGM said below. But outside of that just because of the person I am, I would be there for him emotionally. Suicide is huge in the Army and he all the support he can get while being realistic with him about his actions.

While each situation varies, this is what you can expect:
Local authorities will determine whether or not to prosecute him or have the commander do it.

If it's civilian court, expect he receives a GOMOR, is flagged until the court proceedings finish, and the command may still separate him.

If command prosecutes, it could be Art 15 up to a Court martial depending on the charges. If an Art 15 and reduction, his ETS will he changed to his new RCP, or he will he given 180 days to separate if he's already past the new RCP. 5 years for PFC 8 years for SPC.