Messages to contacts I've been connected with for minimum X days

You can't filter by the duration of existing connections in Sales Navigator.

However, you can export your network list on LinkedIn (https://www.linkedin.com/mynetwork/invite-connect/connections/) using the network export feature (networkexport.smart.compleadly.de).

In the Excel sheet, you'll see a column labeled 'connectedSince,' which shows how long you've been connected.

You can delete any that you don't need and then re-import them into CompLeadly, under the menu item Target Audience ➔ Import Search.

You can then process the target audience using campaign messages or other features.