It looks like bean completions show up at class level, too, and produce weird results. If we show them up at class level (basically as a simplified mechanism to add a new field), it should at least show up consistently and produce correct results.

@Component
public class AnotherTestConfigClass {
    <*>
    
}

This does not cause bean proposals to show up.

@Component
public class AnotherTestConfigClass {
    t<*>
    AnotherTestConfigClass() {
    }
    
}

This shows up bean completions (assuming there are beans with a name starting with t).
Applying the bean completion proposal results in:

@Component
public class AnotherTestConfigClass {
    private final TestBean1 testBean1;
    AnotherTestConfigClass(TestBean1 testBean1) {
        this.testBean1 = testBean1;
    }
    testBean1<*>
    AnotherTestConfigClass() {
    }
    
}

which looks good in general, but the existing constructor hasn't been taken into account.

Interestingly, having the pre-existing constructor public:

@Component
public class AnotherTestConfigClass {
    t<*>
    public AnotherTestConfigClass() {
    }
    
}

causes the bean completion proposals do NOT show up anymore.