There are a couple of options to make the filters more compact, these settings apply to both desktop and mobile views but we can always customize that to only apply to mobile if you want!

You can enable the Mobile accordion in your theme settings, it is often enabled by default on many themes after installation.

There are many options for customizing the Mobile accordion, such as fonts, size, color, and the maximum screen width.

In the theme settings for the Filter Menu you can enable the View More button setting, this will only show the selected amount of filters and then show a button to view all the rest:

Another theme setting that can be turned on is the Desktop accordion, this makes each filter group collapsible and can show all groups open, all groups closed, or just the first group open by default:

You can also select to show the filters in two columns, and/or in small boxes, this setting can be enabled in the Filter Menu app admin, by clicking the 'Display' button on the filter group you want to apply the setting on:

The small boxes can be customized in your theme settings as well.

You could also (this will only apply to your color filters) set the filter display to “Color Swatch“, this will display the color filters as colored circles or squares :

All of these settings could be applied at once, (except for swatches and small boxes) or you can choose one or a few!