I've asked this twice and still haven't gotten a response, so I'll try one more time.
Do you have a full machine backup of the install you are migrating? Are you able to try things on a snapshot?
If you are truly out of the space (or close to it), it's likely that the backup you are taking is incomplete or corrupt because it has run out of disk space.
If you have a full machine backup or snapshot, you could restore it to a machine with more space and do the upgrade there.
If you don't have full machine backup, try mounting another drive and dumping the data to that drive so it's safe. I haven't tried these scripts recently, but should help you backup and restore manually. The only caveat is that you need to restore to the same version of Central on the destination.
central-backup.sh (run on source machine)
#!/bin/bash
set -ex
BACKUP_DIR="/external-drive/central-backup"
mkdir -p "$BACKUP_DIR"
# prevent incoming data during backup
docker stop central-nginx-1
docker cp central-service-1:/etc/secrets/ "$BACKUP_DIR/"
docker exec central-enketo_redis_main-1 redis-cli -p 6379 save
docker cp central-enketo_redis_main-1:/data/enketo-main.rdb "$BACKUP_DIR/enketo-main.rdb"
docker exec central-enketo_redis_cache-1 redis-cli -p 6380 save
docker cp central-enketo_redis_cache-1:/data/enketo-cache.rdb "$BACKUP_DIR/enketo-cache.rdb"
docker exec central-postgres14-1 pg_dump --verbose --format=custom --username odk odk > "$BACKUP_DIR/central.pgdump"
central-restore.sh (run on destination machine)
#!/bin/bash
set -ex
BACKUP_DIR="/external-drive/central-backup"
cd "/root/central"
docker stop central-nginx-1
docker stop central-service-1
docker stop central-enketo_redis_main-1
docker stop central-enketo_redis_cache-1
docker cp "$BACKUP_DIR/secrets/." central-service-1:/etc/secrets/
docker cp "$BACKUP_DIR/enketo-main.rdb" central-enketo_redis_main-1:/data/enketo-main.rdb
docker cp "$BACKUP_DIR/enketo-cache.rdb" central-enketo_redis_cache-1:/data/enketo-cache.rdb
docker exec --interactive central-postgres14-1 pg_restore --verbose --clean --if-exists --username odk --dbname odk < "${BACKUP_DIR}/central.pgdump"
docker compose stop
docker compose build
docker compose up -d