I'm in progress of migrating from Brand X email client to Thunderbird...65.0b2.

In case it isn't obvious, Thunderbird 65.0b2 is a beta version intended for testing purposes, but not for production systems. Did you intentionally install the beta? In case not, download the release version from https://www.thunderbird.net/ and run the installer.

Just in case create a full backup of your Thunderbird profile prior to that. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

In one account, the folders did not sync.

Please explain what that means. What's the account type - POP or IMAP?

I belive the contents currently remain in in Brand X file

What are you talking about?

In case it isn't obvious, Thunderbird 65.0b2 is a beta version intended for testing purposes, but not for production systems. Did you intentionally install the beta? In case not, download the release version from https://www.thunderbird.net/ and run the installer.

Yes, I arbitrarily installed the Beta version.

In the case of one account, which is set up as IMAP in Thunderbird, the files in folders on the server were not downloaded into a local copy. The folders are listed in Manage Folder Subscriptions, but are not created in the local file. The folder contents are now empty online.

My local copy of the emails for the older email program (Outlook 2010 - PST file) appear to still be intact. I wonder if there is a way to re-upload them to the server.

In the case of one account, which is set up as IMAP in Thunderbird, the files in folders on the server were not downloaded into a local copy.

This doesn't happen automatically. You'd need to turn on Synchronization for those folders you'd like to have an offline copy of your messages locally. https://support.mozilla.org/kb/imap-synchronization

The folder contents are now empty online.

I'd assume 'online' means on the server. I don't know what happened to your messages on the server. More information would be needed about the status before, and what exactly you did.

The easiest would be to restore a backup of your messages to Thunderbird Local Folders, and then upload the messages to the server.

My local copy of the emails for the older email program (Outlook 2010 - PST file) appear to still be intact. I wonder if there is a way to re-upload them to the server.

There may be, but I do know very little about Outlook. You may ask in an Outlook forum.

Folder indications do appear under Manage Folder Subscriptions, however selecting them via the checkboxes does not 'stick.'

I'm guessing this is because the folders are no longer actually on the server.

The Outlook PST is a single file containing all the emails and other. I don't have a ready way to get those over into Thunderbird. Maybe there is a way to restore them via Outlook. I'll look into that.

Thanks for your efforts.

You may be able to import messages from Outlook into Thunderbird. See https://support.mozilla.org/en-US/questions/1247226

As said before, make sure to import to Thunderbird Local Folders, and then upload the messages to the server.

Also make sure to create a full backup of your Thunderbird profile before you start messing with it. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

I was able to add an IMAP account on Outlook where I had the Pop3 account. I copied the emails from the Outlook PST account to the IMAP account locally. That managed to register on the server and then the emails were able to be accessed from Thunderbird.