The easiest way is to avoid opening the EML files individually in Outlook. Once you have files spread across multiple folders, that quickly becomes a tedious job.
BitRecover EML to MSG Converter is one option worth checking for this. You can add the complete EML folder, including nested folders, and convert the files in bulk to individual MSG files. It also keeps the folder hierarchy, attachments, formatting, and other email properties, so there is less cleanup afterward. The thread already mentions checking the converted files, and I’d definitely do that with a small batch first.