These errors do not occur when BugSack and BugGrabber are enabled. I assume you have done the same thing I did some time ago, where you always test with these two additional addons enabled and never embedded the library into DialogKey itself. :P

Error 1:
Message: ...-3.0/AceConfigRegistry-3.0/AceConfigRegistry-3.0.lua:12: Cannot find a library instance of "CallbackHandler-1.0".
Time: Mon Apr 1 15:48:27 2024
Count: 1
Stack: ...-3.0/AceConfigRegistry-3.0/AceConfigRegistry-3.0.lua:12: Cannot find a library instance of "CallbackHandler-1.0".
[string "=[C]"]: in function error' [string "@Interface/AddOns/DialogKey/libs/LibStub/LibStub.lua"]:23: in function LibStub'
[string "@Interface/AddOns/DialogKey/libs/AceConfig-3.0/AceConfigRegistry-3.0/AceConfigRegistry-3.0.lua"]:12: in main chunk

Locals: (*temporary) = "Cannot find a library instance of "CallbackHandler-1.0"."

Error 2:
Message: .../AceConfig-3.0/AceConfigCmd-3.0/AceConfigCmd-3.0.lua:17: Cannot find a library instance of "AceConfigRegistry-3.0".
Time: Mon Apr 1 15:48:27 2024
Count: 1
Stack: .../AceConfig-3.0/AceConfigCmd-3.0/AceConfigCmd-3.0.lua:17: Cannot find a library instance of "AceConfigRegistry-3.0".
[string "=[C]"]: in function error' [string "@Interface/AddOns/DialogKey/libs/LibStub/LibStub.lua"]:23: in function LibStub'
[string "@Interface/AddOns/DialogKey/libs/AceConfig-3.0/AceConfigCmd-3.0/AceConfigCmd-3.0.lua"]:17: in main chunk

Locals: (*temporary) = "Cannot find a library instance of "AceConfigRegistry-3.0"."

Error 3:
Message: ...nfig-3.0/AceConfigDialog-3.0/AceConfigDialog-3.0.lua:8: Cannot find a library instance of "AceConfigRegistry-3.0".
Time: Mon Apr 1 15:48:27 2024
Count: 1
Stack: ...nfig-3.0/AceConfigDialog-3.0/AceConfigDialog-3.0.lua:8: Cannot find a library instance of "AceConfigRegistry-3.0".
[string "=[C]"]: in function error' [string "@Interface/AddOns/DialogKey/libs/LibStub/LibStub.lua"]:23: in function LibStub'
[string "@Interface/AddOns/DialogKey/libs/AceConfig-3.0/AceConfigDialog-3.0/AceConfigDialog-3.0.lua"]:8: in main chunk

Locals: (*temporary) = "Cannot find a library instance of "AceConfigRegistry-3.0"."

Error 4:
Message: ...ddOns/DialogKey/libs/AceConfig-3.0/AceConfig-3.0.lua:15: Cannot find a library instance of "AceConfigRegistry-3.0".
Time: Mon Apr 1 15:48:27 2024
Count: 1
Stack: ...ddOns/DialogKey/libs/AceConfig-3.0/AceConfig-3.0.lua:15: Cannot find a library instance of "AceConfigRegistry-3.0".
[string "=[C]"]: in function error' [string "@Interface/AddOns/DialogKey/libs/LibStub/LibStub.lua"]:23: in function LibStub'
[string "@Interface/AddOns/DialogKey/libs/AceConfig-3.0/AceConfig-3.0.lua"]:15: in main chunk

Locals: (*temporary) = "Cannot find a library instance of "AceConfigRegistry-3.0"."

Error 5:
Message: Interface/AddOns/DialogKey/main.lua:91: Cannot find a library instance of "AceConfig-3.0".
Time: Mon Apr 1 15:48:27 2024
Count: 1
Stack: Interface/AddOns/DialogKey/main.lua:91: Cannot find a library instance of "AceConfig-3.0".
[string "=[C]"]: in function error' [string "@Interface/AddOns/DialogKey/libs/LibStub/LibStub.lua"]:23: in function LibStub'
[string "@Interface/AddOns/DialogKey/main.lua"]:91: in function <Interface/AddOns/DialogKey/main.lua:42>
[string "=[C]"]: ?
[string "@Interface/AddOns/DialogKey/libs/AceAddon-3.0/AceAddon-3.0.lua"]:66: in function <.../AddOns/DialogKey/libs/AceAddon-3.0/AceAddon-3.0.lua:61>
[string "@Interface/AddOns/DialogKey/libs/AceAddon-3.0/AceAddon-3.0.lua"]:494: in function `InitializeAddon'
[string "@Interface/AddOns/DialogKey/libs/AceAddon-3.0/AceAddon-3.0.lua"]:619: in function <.../AddOns/DialogKey/libs/AceAddon-3.0/AceAddon-3.0.lua:611>

Locals: (*temporary) = "Cannot find a library instance of "AceConfig-3.0"."

This was fixed by 373854b, but I never pushed the release tag, woops!

The entire repository was reverted to v1.5.7, is probably why, I haven't had the time to look into why the 1.6 code was removed.