Bluetooth mouse generates keyboard code but doesn't trigger

I have a unique handheld trackball mouse that I love (Elecom Relacon Handheld Trackball Mouse Thumb Control 2.4GHz Wireless); it features media control buttons (forward, backward, play/pause, volume up, and down).

Since I'm using its Back/Forward buttons as left/right key shortcuts (to go back and forth 5s on videos like YouTube, which are used way more frequently than web navigation) I want to use the media forward and backward buttons to navigate Chrome history to go forward/back.

After testing with BTT's advanced conditions window, it appears that the media buttons on the mouse behave like keyboard events, and condition currently_pressed_keyboard_keys CONTAINS "1018" and ...CONTAINS "1017" changes to "Currently True" when pressing the respective buttons.

I thought "got ya!", but after assigning them to Chrome's shortcut (or anything else, really) they don't trigger. And in a sense I get it, as there's no recorded mouse button to trigger it, since clicking these buttons on the BTT mouse config does nothing (as opposed to clicking regular mouse buttons like left click or forward)

Clicking media go back button on mice:

Setting the same triggers in the keyboard don't trigger either (I'm assuming similar issue: no key trigger directly assigned as I just know the keycode). The legit keyboard's media back/forward buttons have different key codes (1020 and 1019).

Don't know how to get it right.

Thank you everybody in advance.

so I’m not completely sure whether you already tried, but can you check whether they do record something when you add a new trigger in the keyboard shortcut section in BTT?