I believe that the message you received reads that the default backup directory is in use. This is not an error, it's a warning, and presented as such — with the explicit note that you can backup your site. The message itself links to a page which explains that this is only a minor, potential security issue on a minority of live web hosts where all other mitigations we have in place have failed. Since you are on a local server you can of course use the default output directory.
Moreover, you said that “I could have created another directory per Akeeba docs but that doesn't solve the problem” which, as phrased, is wrong for two reasons. First, you imply you didn't try it. Second, creating a different folder is not enough; you have to tell Akeeba Backup to use it as per the documentation. But wait, there's more.
Since you are on Windows and using XAMPP, you need to remember that XAMPP does not run under the same user account as you are logged in. Therefore, any folder or file that you create (e.g. through Windows Explorer) will not be writeable by the web server. You will have to give it the right permissions. This is not something new. That's how XAMPP has been working for well over a decade*. Since your server is not exposed to the Internet, the easiest way is to give all permissions to Windows' Everyone user. Right click on the folder in Windows Explorer, select Properties and click on the Security tab. Click on the Edit... button. If you can't see a user named Everyone, you will have to click on the Add... button, type Everyone in the big text box and click OK. Now click on the Everyone user and then take a look at the list of checkboxes below. Click the Accept checkbox on the Full Control row (the topmost one). Click on OK, then again on OK.
If you do not believe me, there is a very simple method to be convinced. Uninstall Akeeba Backup from your site. Download the previous version (9.6.1, released a month ago). Install it. You will have the same problem. I think it's fairly obvious that it's impossible to have a broken version out there for a month, with tens of thousands of sites unable to take a backup, for we had stopped existing as a company to put it plainly. Ergo, the root cause is misunderstanding the information on your screen and not taking Windows permissions into account.
* Side note about XAMPP. Back in the late 00s / early 10s (around the time Windows Vista and 7 which introduced permissions checks even in the Home versions) it would still install in C:\XAMPP (just like it did when Windows XP was around) and its directories would be owned by your Windows user. As a result, you never had to deal with permissions. Starting in the early 2010s (late Windows 7 era, early Windows 8 era) XAMPP gave an option to be installed in C:\Program Files (x86), and its services (Apache and MySQL) would no longer run under your Windows user, nor its folders be owned by your Windows user. This led to issues with permissions. It became a problem restoring sites which is why I wrote this page: https://www.akeeba.com/documentation/akeeba-kickstart-documentation/kscantextract.html#kstslocal. Sometime in the mid-2010s (I think it was around 2015, if memory serves) it started defaulting to be installed in the Program Files directory. This has confused people to no end ever since.
Nicholas K. Dionysopoulos
Lead Developer and Director
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