The spec (https://cr.openjdk.org/~abimpoudis/unnamed/jep443-20230322/specs/unnamed-jls.html) says:

SwitchLabel:
case CaseConstant {, CaseConstant}
case null [, default]
case CasePattern{, CasePattern } [ Guard ]
default
CaseConstant:
ConditionalExpression
CasePattern:
Pattern
….
 
Pattern:
TypePattern
RecordPattern
TypePattern:
LocalVariableDeclaration
The following productions from 4.3, 8.3, 8.4.1, and 14.4 are shown here for convenience:
LocalVariableDeclaration:
{VariableModifier} LocalVariableType VariableDeclaratorList
VariableModifier:
Annotation
final
LocalVariableType:
UnannType
var
 
And JDK-8307444 says:
Neither the unnamed pattern nor var _ may be used at the top level of a pattern, so all of these are prohibited:

    ... instanceof _
    ... instanceof var _
    case _
    case var _

So, using var _ in nested patterns should be accepted by the compiler.

But this code fails:

record TestRecord<T>(T a) {}
    private static <T> int consume(T t) {
        return switch(t) {
            case TestRecord(var _), TestRecord(Integer _) : { //java: as of release 9, '_' is a keyword, and may not be used as an identifier
                yield 1;
            }
            default : {
                yield -2;
            }
        };
    }

    public static void main(String argv[]) {
        System.out.println(consume(new TestRecord("test")));
    }

java --version
java 21-internal 2023-09-19 LTS
Java(TM) SE Runtime Environment (build 21-internal-LTS-2023-04-30-1558228.angelos.bimpoudis.dev)
Java HotSpot(TM) 64-Bit Server VM (build 21-internal-LTS-2023-04-30-1558228.angelos.bimpoudis.dev, mixed mode, sharing)