Your new provider is right - do not cancel your PlusNET service because of the way BT Openreach business systems work that will impinge on the new ISP’s ability to place orders.
However you MUST advise Plusnet that you plane to move away but wish to retain your email service. There is no longer a fee for mail only accounts.
When you move, your account will be destroyed and recreated, requiring you to rebuild the mailboxes through the user portal after which Plusnet will restore the mailbox contents. It is therefore wise that you get a record of the email addresses before hand. Not is issue if you only have one or two but some users have lots.
For your purposes, use the “I’m thinking of leaving” option - that has a dedicated team and wait times are usually shorter.
Yes repossess times everywhere are protracted at present - but do you actually have a problem which makes that an issue? Service migration has risks to continuity.