Thanks for the update. Since your personal OneDrive is showing less than 0.1 GB used out of 1 TB, that strongly suggests the missing spreadsheets are probably not currently stored in that personal OneDrive account, unless they were deleted, moved, or saved somewhere else originally.
At this point I would separate the issue into two parts:
First, for the Excel sign-in loop on the iPad, please try clearing the saved Office credentials from iPad settings, not only uninstalling the app. Go to iPad Settings > Excel > Reset Excel, then enable Delete Login Credentials. After that, fully close Excel, reopen it, and sign in again with the personal Microsoft account that owns the subscription.
Second, for the files, please continue checking the storage locations directly, not only Excel’s Recent list. The Recent list can disappear or change when the app credentials/cache are reset, and it is not the actual storage location. Please check:
Personal OneDrive on the web: My files, Recent, Recycle Bin, and Personal Vault if used.
Work OneDrive on the web: My files, Recent, Recycle Bin, and any SharePoint/Teams locations your organization uses.
The iPad Files app: Browse > On My iPad, iCloud Drive, OneDrive, and Recently Deleted.
Search by partial file names or by “.xlsx” instead of relying only on the file names shown in Excel Recents.
If you have an active Microsoft 365 subscription and you are sure these files were stored in your personal OneDrive, you can also try restoring OneDrive to a previous state.
https://support.microsoft.com/en-US/onedrive/restore-your-onedrive-files