These are pretty in depth questions and really should be answered as part of a consultancy rather than these forums. Not that many of us cannot answer them its just not exactly the scope.
You asked
I want to understand which approach works best when implementing D365 integrations—whether standard connectors in Power Automate are sufficient, or if Azure Logic Apps provides better reliability, performance, and flexibility for advanced or high-volume scenarios.
There is no way to answer this because we have no idea what you are connecting too. Standard connectors what does that mean? Connectors that are actually licensed as Standard or do you mean standard in a generic way and you include Premium connectors in your question?
Comparing ALA versus PA requires much more specifics as anything else is generic and not really a best practice or architectural guidance, because I might not pick either depending on your actual requirement.
You also asked
Additionally, I’m looking for guidance on when to use custom connectors, message queues like Azure Service Bus, or API-based integrations for building a long-term stable architecture.
Again too generic, but custom connectors as you can read about are clear. They are for scenarios where an existing connector doesn't exist to API's etc you want to connect too, or you want to extend an existing one that is limited to what it provides
As for building long term stable architecture, ASB or APi really is not where I go, I go to what are you scenarios and business use cases. ASB is great if you want to build Async processing from D365 to something else. If you want real-time and as long as you can make it happen in the proper timeouts, then calling API's from plugins, embedding HTML web sources etc all work.
But sincerely, when we are talking about building architecture guidance for a business a forum is not the right place because there are way too many gaps. Real answers come from details and details come from decades of experience to know to ask the right questions about your business, industry, systems you leverage, number of users, internal, external and so much else.
Cheers