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That sounds a lot like a generated file and not like anything you're supposed to lay your hands on.
The proper way would be to provide your own theme - this might be in the admin/control-panel theme, but I can't say for sure.
Plus, with regards to changing a min-width property: Do you see a width of less than 10 px to determine that your change doesn't work?

The proper way is to overwrite that file with a theme contributor. See https://help.liferay.com/hc/en-us/articles/360028726532-Packaging-Independent-UI-Resources-for-Your-Site. The issue with this method is that it will affect all Product Menus across all your sites. If you need the Product Menu styled specifically for a site, the best way is through the theme like Olaf mentioned.
Liferay Portal uses two themes, one for your public facing site and one for the admin section. Just a warning, the Product Menu styles can vary between public and admin if you don't apply your changes to both themes. To change the width of the Product Menu in your theme's _custom.scss:
@include media-breakpoint-up(sm) {
    body.open.has-control-menu {
        .control-menu {
            left: 100px;
        }        #wrapper {
            padding-left: 100px;
        }
    }    .lfr-product-menu-panel.sidenav-menu-slider:not(.lfr-admin-panel) {
        &.open,
        .sidenav-menu {
            width: 100px;
        }
    }
}
or Go to your site > site builder > pages > public pages cog icon > Insert custom CSS that is loaded after the theme
This method only applys the Product Menu styles for the public facing site
@media (min-width: 576px) {
    body.open.has-control-menu .control-menu {
        left: 100px;
    }
    body.open.has-control-menu #wrapper {
        padding-left: 100px;
    }
    .lfr-product-menu-panel.sidenav-menu-slider:not(.lfr-admin-panel).open,
    .lfr-product-menu-panel.sidenav-menu-slider:not(.lfr-admin-panel) .sidenav-menu {
        width: 100px;
    }
}