Is there any way to get IntelliSense working with Azure Data Studio to get linked server references from SQL server?
I am getting Invalid object name on linked server references in my queries.
Ctrl+Shift+P => 'Refresh IntelliSense Cache' doesn't fix it.
Intellisense does not offer this feature; this is true in both Azure Data Studio (ADS) and SQL Server Management Studio (SSMS). This most likely because caching such information could be quite slow, as linked server connections themselves can be quite slow, and any caching would be completed over the linked connection; for a linked instance with many objects that could be a lot of traffic.
There likely is some kind of extension that might offer the service. I know that, for example, Redgate's SQL Prompt offers caching of objects in linked servers in its version of intellisense in SSMS, however, that feature is not in their ADS extension. As ADS is also open source, and "easily" extendable, you could also consider writing your own extension, if you feel the need, have the expertise, and the time.