How do I retain edit settings after re-importing?

Thank you for this.

Photoshop does not retain your RAW edits. Adobe Camera Raw does store the edits you do in a sidecar file. If you delete this file, your edits in ACR will be gone too.

Lightroom uses a database and deleting a picture in Lr basically deletes the data associated to that picture (ie your edits) and eventually, depending on your answers, also the file itself.

Fortunately, Lightroom asks at regular intervals for database backups to be done. If and only if you have such backups, you may get back all of your edits except the latest, done after the backup. The Lightroom Queen is a great source for Lightroom information. Here is probably the article you will need for restoring your edits: https://www.lightroomqueen.com/partial-restore-backup-catalog/

The reason that your edits to Raw files made from Photoshop were remembered, was because when you clicked "Open" (or "Done", but not "Cancel") from the Adobe Camera Raw dialog, some updated metadata describing your latest conversion settings, were written alongside the Raw file on disk. In the case of a proprietary Raw file, that means in a sidecar file with the extension ".xmp". In the case of a DNG file, or in the case of a bitmap file (such as JPG) which has been opened into ACR, those conversion settings are stored within the main image file.

When you return to the same Raw again, using ACR, those settings are found on disk and shown to you once more.

If you were to import such a file to Lightroom, the same thing would happen - in that these conversion settings would be copied into the Catalog, and thereafter remembered (and adjusted further) but without needing to go back to the disk for those.

That said, Lightroom can also be told to write updated metadata back to disk ALSO - as well as within its own Catalog. ACR and LR are intercompatible, provided they are of the same generation, in that they will understand these conversion settings identically.

To reiterate: this writing of edits back to disk is as well as, rather than instead of, using the LR Catalog. You can set LR to do this automatically, immediately after making each change to an image, otherwise it will only do that on your explicit command. This is an option in the Catalog Settings iirc.

If you had written your edits to disk, previously, then deleting and reimporting the images would not have lost those edits.

However, it is much better to simply correct any wrong addressing, of folders or images (better still to avoid that in the first place of course, by simply leaving things be on disk). There is more useful information held about an image within the Catalog, than CAN be written to disk - most particularly, Virtual Copies but also Collection membership plus a few other LR specific features which have no direct equivalent in Adobe Camera Raw. Such as, your sequential editing History.

If you have a previous backup, unzip the dated folder and double-click the named catalog (ending .lrcat) to launch in Lightroom.

Go to the folders panel and right-click on the folder name and choose “update folder location” and then navigate to the folder where the images are stored.