Might need a bit more info.

I'm not a Thunderbird user but set it up to see if I could replicate the problem.  I have a GSuite account (so GMail) and I set up the connection to use IMAP. When I created a folder a category was created in GMail. When I deleted the folder in Thunderbird it the category was moved to the Bin in GMail. When I deleted it from the bin (in Thunderbird) it was removed from GMail.

So IMAP to Gmail definitely works. Things will likely be quite different if you're using POP3.

Screenshot please.

The ultimate way of deleting things on Windows that are hard to delete is to boot a live Linux image and use that to mount the windows partition.  Then you do "sudo su" to get a root prompt and from there you should be able to delete anything.

Once you have sorted the issue you could consider a portable version of Thunderbird. For a least the last 10 years both the program and data have been stored in a single folder on D drive. Now more than 4GB.

It can easily be backed up to a USB drive and run from any PC.

All much easier for me.

This is an internal Thunderbird issue. It has nothing to do with Windows or anything else although I am using the Windows version. Thunderbird is the email client I use. I have several email accounts installed on it. Each account displays Inbox, Sent Mail and Trash, which is how I have it set up. For some reason one account has somehow added a new Thunderbird (not Windows) folder called 'Templates'. It is empty but for some reason, it seems to be almost impossible to delete. This is only a minor annoyance, nothing more, but it gnaws at me. I have looked it up on the Thunderbird site but I still can't figure it out. I was hoping a more knowledgeable user than me would know a trick. 

Unleashing a Linux canon on this would be a bad idea. This is a Thunderbird issue and I don't want to lose my emails. There needs to be a Thunderbird way to fix this. 

Which email provider has this folder?

You say you created it, but could it be a folder defined by your email provider that cannot be deleted?