Thank you very much for your response. It may indeed be due to the "Legacy" option, but I'm still unclear about the specific effects of using "Legacy". This is because I'm not familiar with how the ValueQ function behaved in previous versions. Additionally, I'm puzzled as to why ValueQ[a[b]] returns True, even though a[b] itself hasn't been assigned a value.

Is there any documentation available for older versions? Or is there another method to understand how ValueQ worked in previous versions? I noticed in the "History" section it only mentions updates to the function, but where can I find specific details about what those updates entail?

The documentation (http://reference.wolfram.com/language/ref/ValueQ.html) seems pretty clear. ValueQ takes a Method option, and Method has 5 choices: Automatic, "SymbolDefinitionsPresent", "TrialEvaluation", "OwnValuesPresent", and "Legacy". I think the answer to your question is found in the documentation for "Legacy": "match behavior in Version 12.1 and earlier".

The way I understand the documentation, ValueQ[a[b]] gives False because a[b] has no value, in the sense that you never defined a[b]=something; iif I enter a[b] I get back a[b]. Your definition a[b][1] = x defines a subvalue, not a value, of a[b]. Try ValueQ[a[b][1]].