So to summarize, a not-working device was acquired from a company that seemingly can't afford to support their products at the prices that they can charge for their wares, and you're now presuming that the problem lies with a second entity—though the first bunch explicitly claims support for the macOS software configuration you're using—and are asking a third bunch—a third bunch that lacks access to this hardware—for help.
I'd start by removing what has been installed, and installing the simplest of options available from Logitech for the M510, and see if that works.
I see at least three different software packages that reference this mouse, which is unexpected. That's a lot of redundancy, and that's a lot of software to maintain and test.
If you really want the Unifying software, also try the previous 1.2.359 version, which also indicates support for High Sierra.
I'd also tend to avoid any mouse that required extensive drivers, and devices that seemingly aren't using Bluetooth or USB for the connection. I'm also skeptical around what (else) some of the vendors of add-on drivers are accessing and might be uploading, but that's a generic skepticism around how some of the vendors of cheap devices are accruing their profits.
And yes, have a look at OverDrive.