Additional features, settings, or issues not covered by specific Microsoft Teams Free categories
Meeting recordings with a personal account are only saved to Cloud, nowhere else. A link to this recording file should be available in the meeting chat. If there is no link available, then the recording was probably not successful. One of the reasons for a filed recording can be that you have left the meeting without first stopping this recording.
You can try to export your entire chat and files history from the Cloud and look for this recording file in the export file.
https://teams.live.com/dataexport/
If available, the recording file will be present in the \media folder as a .mp4 file.
Follow these instructions on how to download and extract the export file.
Note also that if you are on a Windows 11 computer with the latest updates, then the .tar export file can be extracted directly in Windows File Explorer.