Moving Time Machine to new disk after disk issues

Apple has instructions for this, it's basically copying the complete Time Machine backup folder from the old drive to the new drive and continuing from there with the new drive. Apple specifically says to do the copy using the Finder, not some other method (you used another method). See this article

https://support.apple.com/guide/mac-help/if-the-time-machine-backup-disk-is-full-mh15137/10.15/mac/10.15

That said, Apple's instructions presume that your old Time Machine backup drive is clean and uncorrupted. Since yours is corrupted, unpredictable results may ensure if you try to copy it. In fact you already noted that some permissions were incorrect and a somewhat elaborate method (which ultimately did not work) had to be tried to do the copy.

For those reasons, I suggested not trying to copy the old backups, instead just keeping that drive for emergencies only but start a new backup series on a new disk. This is triaging a non-ideal situation. I would format and re-check your new disk anew also, it sounds like it has been corrupted from something on the old bad one?

What I have started doing is using TWO Time Machine external drives. When there are two, Time Machine simply alternates between them for the backups. So each one has backups every two hours, offset by one hour. This ensures that if a Time Machine disk goes bad (they all do eventually if you use them long enough ...) you can continue with the full history on the other backup disk while you are arranging to replace the failed one.

I have seen this type of behavior with external USB drives when they fail. They sometimes appear as "read only" at that point and when Disk Utility First Aid is run (to try to repair the faulty disk) it either cannot repair it or First Aid itself freezes.

The reason the external disk takes so long to mount is that fsck is run automatically by the MacOS when it detects a disk with a corrupted file system, which it probably has. Running fsck can takes several minutes or even many minutes if/when errors are encountered (which has no doubt happened in this instance) as it will try to repair and rerun.

My experience is that such disks are no longer reliable and should ultimately be discarded. You can keep it for a while since it does have backed up copies of your files but it is no longer a reliable disk. You need a reliable disk for a backup.

If the power failure caused the damage there might be physical damage, as well as a corrupted file system.

I suggest immediately procuring a new external disk for backups and starting a new Time Machine backup on it. While that new Time Machine disk won't have the history of your earlier backups, your faulty disk does and it appears that you can at least read files and copy them from it for now.

My approach to these external drives has evolved over the years. I used to invest in time, energy, software tools etc. to try to "repair" them. No more, if Disk Utility or TechTool Pro cannot fix it, I'm done. I now consider them as consumables, much like a battery, eventually they will all wear out. Some last 10 years or more, some wear out after several years. They are inexpensive (under $100 typically) so I find that the hassle of trying to get prorated reimbursements via warranties, etc. is not worth it, the postage for returning the drive is often a good fraction of the cost of the drive! However I do buy drives only with warranties that are 3 years or more (5 years if I can find them), I figure that increases the odds of a higher quality product and lower likelihood of failure.