Your old site is still on the old database engine that Joomla used to use. Your new site is using InnoDB, but your host did not configure it correctly causing you to hit a row limit of 8126. The only real fix for this is to have InnoDB configured correctly with the below database settings.
innodb_large_prefix = 1
innodb_file_per_table = 1
innodb_file_format = Barracuda
Aside from that you can try deleting a few columns from _cbsubs_plans that are not being used and change varchar columns to text columns once the error stops and allows you to do so. Once those have been changed from varchar to text you can rerun the tools check to recreate the deleted columns.
In short due to server configuration your row size limit is half of what it should be. Also if your host is using MariaDB instead of MySQL then see the below for configuration settings.
www.joomlapolis.com/forum/153-professional-member-support/242484-installation-cb-connect-failed?start=12#318734
This often happens when a host does not maintain database configuration and ends up having default values from over 4 years ago or they're intentionally trying to limit row sizes to reduce storage space. Using such settings however puts the database out of default spec making it impossible to develop for as we have to develop for defaults.