A family member has updated their MacBook Air from the latest version of Mojave to Catalina 10.15.1.
The MBA has got a 250GB SSD drive, of which only 80GB are in use (170 available). They've been backing up the MBA with Time Machine more or less regularly, with the last backup completed 7 days before the upgrade. (I know, I know: they should have backed up right before upgrading, but now it's too late for that) The Time Machine drive is an external hard drive connected via thunderbolt (v1) cable and thunderbolt to USB-C adapter.
Now the upgrade to Catalina has completed successfully, but they can't backup to Time Machine anymore because "there isn't enough space".
The Time Machine drive is a 1TB hard drive with 505GB available. That should be plenty to perform a new incremental backup of the MBA. I know that backups following a major macOS update take more space, but it should still fit comfortably in 505GB, and even if it didn't it should automatically clean old backups.
Is it a genuine issue (it actually needs more than 500GB), or an error? How do I fix it without losing the old backups?