WordPress’ work or execution flow manipulating $wpdb

I am not sure if I understand your question right but you seem to misunderstand a bit how PHP requests are typically executed.

$wpdb is not persistent, it belongs to specific page load and only exists while that page load is being performed. Unless your code always changes it – independent second (third, etc) page load will have its own instance of database connection.

Same applies to actions – they are executed in the context of specific page load, not in any kind of global persistent way.