Ignore all my advice, please. I do not know what DEVONnote is or anything about it. I thought it an erroneous autocorrect or something.
Were your databases encrypted? If not, the would be called .dtSparse; find you database(s) on the backup disk, copy them to a pertinent location on the hard drive in your Mac (e.g. /users/yourusername/databases or /users/yourusername/documents/databases) and simply open them. They will load in DEVONthink 3. No need to migrate, import or anything.
Ah, I made the same mistake, overlooking that you wrote note rather than think; I donāt know whether the databases were called .dtSparse in the day, and Iād guess not. @BLUEFROG would know, though.
I believe itās just a subset of DEVONthink, now discontinued.
this post suggests where you might find the DEVONnote database: Your database is the folder named DEVONnote at ~/Library/Application Support/
The rest of the entries in the forum suggest that you will not be able to open the database with DT3; the posts all suggest exporting from DN2 and importing into DT3. If that is the case (simply try and see), and if you donāt have the installation file for DN2, it may be available for download in you DEVONtech user account. It might not work on Big Sur however - Iām not sure from what Iāve read.
Ah, that sounds hopeful. But a quick try brought up a new gotcha (for me) - how do I open ~/Library/Application Support/ on the external hard drive? Option > Go opens it on the iMac, not the external drive.
If you use CMD + Shift + . then hidden files will become visible (same to hide them again); that way youāll be able to see the ~/library folder in Finder
~/library is a subfolder under your user home folder. /library is a system folder under the root. two different places. take care.
once found on the external drive you can drag and drop where you want on the new set up. i suggest you do this with two Finder windows.
Okay, I can now see my home folder library! Progress. In Application Support > DEVONnote 2 thereās a series of files called DEVONnote-1.dtMeta, up to number 10. (There are also have some Backup folders in there but they would be earlier.)
In that case I donāt think youāll be able to import directly. It might be easiest to boot from your bootable external drive, run DEVONnote, and export the files as suggested e.g. here, then boot your Mac from its internal drive and import the files into DT3.
From what I can find in the forum dtMeta files are the metadata, not the data itself.
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Iāll try that. Maybe not tonight (Iām in the Canary Islands and itās getting a bit late here) but tomorrow. Many thanks to both for the help so far. Iāll report back.
19:16 sounds like a great time for another glass of wine, starting a Mac from an external drive, another glass of wine, exporting some data, another glass of wine, copying data, a brief walk, a day dream at the ocean front, another glass of wine and - well, after that much wine, who knows?
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ā¦and who cares?!! But Iāve just had a terrible time with my update to Big Sur (donāt ask) and Iām nervous of making mistakes. Glass of wine, though, yes. Cheers.
enjoy 
Sorry to hear things have been playing up for you; Iām sure together weāll get you up and running DEVONthink 3 though
As the helpful others have been suggesting, yes the ~/Library/Application Support/DEVONnote directory is the entire DEVONnote database. The Backup folders in there are internal metadata backups, not file backups.
There isnāt a direct import but yes you can do the File > Export > Files & Folders and import those files into DEVONthink.
Long ago, I had written a script to convert a DEVONnote database to a DEVONthink database. I wonder if it still worksā¦
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Many thanks for your response. I have now successfully imported my data into DEVONthink! This is obviously a diminishing need but still, in case anyone else might find it useful, this is what I did in step-by-step detail.
Stage 1: if necessary, import your original data into a new installation of DEVONnote
1 Install DEVONnote 2.11.2 on the Mac if itās not there already ā legacy software but still available for download. (This may not be essential ā see note 1 below.)
2 Plug into the Mac the USB hard drive carrying your backup.
3 On this backup hard drive find the folder ~/Library/Application Support/DEVONnote 2 and copy it to a convenient location on the Mac ā in my case, the Desktop. (For how to find the ~/Library/ folder see note 2 below.)
4 On the Mac, find the equivalent folder from the new installation of DEVONnote 2 (~/Library/Application Support/DEVONnote 2) and delete it, then replace it with the one just copied from the backup HD. (Make sure to quit DEVONnote 2 before you do this.)
5 Launch DEVONnote 2 on the Mac, which will now show your data.
Stage 2: export the data from DEVONnote 2
6 In the sidebar of DEVONnote 2, select a folder or an individual file (see note 3 below).
7 File menu > Export > Files & Folders to the Desktop or any other folder.
8 Export the other folders and files in the same way.
Stage 3: import the database into DEVONthink 3
9 Launch DEVONthink 3 then File menu > Import > Files & Folders to import those youāve just exported from DEVONnote 2.
Note 1: If you have a bootable backup hard drive with DEVONnote 2 already there, you could start up the Mac from this drive (Option-start) and save the database folder to another external device.
Note 2: Useful tip I learned during this exercise: Command-Shift-[.] reveals the hidden files including your user Library. So easy when you knowā¦
Note 3: You canāt export the whole lot in one go, only individual folders or files.
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As per this post from 2009 it should be possible to select all the content for export using Command-A. As far as I can determine, DEVONnote 2 was current at that time.
Thanks for taking the time to write up what you did 
Youāre welcome and thanks for sharing your process and findings.
And indeed, @Blanc is correct. Command-A in the item list is the shortcut for Edit > Select All (a shortcut common to many apps actually).
Cheers!
Yes, apologies, my mistake. You can also select a folder then shift-click another further down the list to select all those in between.
No worries at all!
And indeed Shift-selecting is possible.
Command-selecting can also be used for non-contiguous selections
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