Keep in mind that Lawnchair is buggy and consistently 2 years behind the latest version of Android. I'm using their 12.1 beta, and it still crashes with null pointer exceptions about twice a week. And, on Android 13 and 14, integration you would expect between the recents screen and Lawnchair does not work. These are the gestures you're talking about.
And here we are on the launch of Android 14, with no development of Lawnchair for Android 13 in sight.
I should also point out, these gestures you're mentioning only work on the stock Pixel launcher, the AOSP launcher, and Lawnchair. This is because starting with Android 9, Google baked the recents switcher directly into the launcher app. And, it has to be a system-level app with a special system config that allows the launcher to perform this function.
This is why root is needed for the Quickswitch module. Lawnchair has the code to do this (at least on Android 12), but you have to overwrite a system config to allow Lawnchair's package name to be capable of serving the recents screen.