The error code basically says "no data", which is probably caused by not adding any data to the disc using CDBurnerXP. It doesn't have a "finalize only" feature. But you can check the disc information window to find out if the disc is indeed not finalized.
After 20 years your discs might also have become unusable. Since DVD+R are not particularly uncommon, the situation you describe might be an indiciation for this having happened. Again, you can use the disc information window to determine whether any data can still be detected on the disc.
If you look for more permanent storage options, have a look at M-Disc or cloud storage.