LedgerBegin on pruned ledger

Does “LedgerBegin” represent the beginning of the ledger or does it represent the earliest availabie offset in the case of a pruned ledger?

LedgerBegin is the beginning of the ledger not the latest pruned offset. If your ledger has been pruned requests for that will fail. There is a GetLatestPrunedOffset endpoint on the transaction service that you can use to get the earliest available offset.