Coditions:
Confluence cloud; new sidebar navigation; app web-item wich placed under Apps dropdown does not open dialogmodule (Even tried dialog as target type and got the same result).
Here is what I see when click on my btn 
Here is configuration in atlassian-connect.json
"webItems":[{
"location": "system.header/left",
"weight": 200,
"icon": {
"url": "{path}"
},
"target": {
"type": "dialogmodule",
"options": {
"key": "my-dialog"
}
},
"key": "my-dialog-btn",
"name": {
"value": "Click me"
}
}]
"dialogs":
[{
"url": "/advanced-link",
"options": {
"size": "maximum"
},
"key": "my-dialog",
"conditions": [
{
"condition": "user_is_logged_in"
}
]
}]
I have exact the same config on Jira plugin and it works as expected.
Also have compared links after click and they are different:
Old top nav:
{baseUrl}/wiki/plugins/servlet/ac/{appKey}/my-dialog-btn
New sidebar nav:
{baseUrl}/wiki/plugins/servlet/ac/{appKey}/{appKey}__my-dialog-btn