Can I please clarify something. You said
I am encountering the following error when attempting to import a solution into our client tenant. Prior to the import, I configured the required connections and environment variables. I also ensured that all relevant tables and dependencies were included in the solution
This makes it sound like you are going INTO their environment and creating things prior to importing, You should not do this. All resources should be part of your Managed Solution. P.S. The only time you would do unmanaged if you were "building it for them and now handing it off to their dev environment"
So if you are manually creating stuff in advanced I am certain you are causing issues.
So what you should do
Clean up their environment, uninstalling, and going into the Default Solution and deleting anything you created
1. In your solution make sure you have do the "add all dependencies" to make sure you aren't missing anything that should go in your solution
2. Make sure your Environment variables default values are cleared
3. Make sure to run solution checker
4. Export as Managed
5. Make sure to use Connection References in flows not Connections
6. Make sure that if you have a canvas app, and if you turned on Auto Create Environment variables, that you add them to the solution as they will not be by default as they are considered System Default's not Solution Aware Defaults
7. Always let the the Import create new connections as necessary and after import or during set the Environment values for that environment
If these suggestions help resolve your issue, Please consider Marking the answer as such and also maybe a like.
Thank you!
Sincerely, Michael Gernaey