The Joomla version is irrelevant. The backup engine is used in Akeeba Backup for Joomla, Akeeba Backup for WordPress and of course our standalone backup application Akeeba Solo. It does not rely on Joomla. Do note that I have been developing on Joomla 6 since its Alpha 1 version many, many months ago. My main dev site is Joomla 6 on PHP 8.4 and I also test on a combination of Joomla 4.4, 5.4, and 6.0 on PHP versions 7.4, 8.2, 8.4, and 8.5. That is to say, it's not your Joomla or PHP version; it's what I am using as my main dev target and I would've caught any issues months ago.
Moreover, there has been no update in Akeeba Backup in the last couple of months. Most importantly, the last time we updated the code for WebDAV was May 2023, over two and a half years ago. So, it's not a change in the code that has anything to do with it.
I tested it anyway on a Joomla 6.0.1 site running Akeeba Backup 10.1.0 on PHP 8.4.15 which is pretty much the configuration you are using. My target is a WebDAV server created on a cPanel-based site hosted by Rochen using cPanel's "Web Disk" feature. No problem at all. My 200 MiB backup (20 files of 10 MiB each) uploaded just fine.
The message you get means that your WebDAV provider replied with an HTTP 401 response. This comes from them, not us. They did not like the username and password you sent them. If you are sure your username and password is correct (Test it! Do NOT assume it's correct just because it used to work!) then the problem is either with your host, or your WebDAV provider. I can't help you with this. It's not under my control.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!