Use AddJsBlock to set and add a JS block.

var jsAction = new CustomActionEntity()
{
    Name = key,
    Location = "ScriptBlock",
    ScriptBlock = scriptBlock,
    Sequence = sequence
};

UserCustomAction targetAction;
    UserCustomActionCollection existingActions;

var site = (Site)clientObject;

existingActions = site.UserCustomActions;
site.Context.Load(existingActions);
site.Context.ExecuteQueryRetry();

targetAction = site.UserCustomActions.FirstOrDefault(uca => uca.Name == customAction.Name);

targetAction = existingActions.Add();

targetAction.Name = customAction.Name;
targetAction.Description = customAction.Description;
targetAction.Location = customAction.Location;
targetAction.Sequence = customAction.Sequence;

targetAction.ScriptBlock = customAction.ScriptBlock;
targetAction.ScriptSrc = customAction.ScriptSrc;

targetAction.Update();
if (clientObject is Web)
{
    var web = (Web)clientObject;
    web.Context.Load(web, w => w.UserCustomActions);
    web.Context.ExecuteQueryRetry();
}
else
{
    var site = (Site)clientObject;
    site.Context.Load(site, s => s.UserCustomActions);
    site.Context.ExecuteQueryRetry();
}

bool success = site.AddJsBlock(key, scriptBlock, 0);