Below are the answers of your questions according to my knowledge
- Hover card functionality is only available user value not for group value
- There is no way to get group members using column json formatting.
Workaround 1
You can create custom field customizer using SPFx.
SPFx Extension Samples
Workaround 2
You can render user field in such a way that in case of user value it renders with hover card (which is default functionality) and in case of group value you can generate hyperlink which can redirect user to group page where user can see members of the group.
Following is the JSON for the same. Here in order to identify whether it's group or user I used sip property to identify it because in case of group, sip will be always empty.
{
"$schema": "https://developer.microsoft.com/json-schemas/sp/v2/column-formatting.schema.json",
"elmType": "div",
"children": [
{
"elmType": "span",
"defaultHoverField": "@currentField",
"txtContent": "@currentField.title",
"style": {
"display": "=if(@currentField.sip == '','none','block')"
}
},
{
"elmType": "a",
"style": {
"display": "=if(@currentField.sip == '','block','none')"
},
"attributes": {
"href": {
"operator": "+",
"operands": [
"@currentWeb",
"/_layouts/15/people.aspx?MembershipGroupId=",
"@currentField.id"
]
},
"target": "_blank"
},
"txtContent": "@currentField.title"
}
]
}
Below is the output of column formatting:

Official Documentation: https://docs.microsoft.com/en-us/sharepoint/dev/declarative-customization/column-formatting