Remote control through Websocket will always work, because a socket connection isn't restricted by being admin or non admin. Only the hotkey transport mechanism within Windows is restricted by Windows.
This brings up a related issue. Hotkeys can also be artificially generated by mouse or keyboard companion apps like the widely known Logitech Gaming Software. For these companion apps, the same restrictions apply as with OBS, only the other way round. These cannot send (generate) hotkeys to an app running as admin, as long as they are not themselves running as admin.
This means, if you start OBS as admin, you need your companion app to start as admin as well. Otherwise you cannot generate hotkeys that OBS will recognize.
For example, if you have a MMO mouse with 12 keys and assign some of these keys in your companion software to send the hotkey for start/stop recording or switch to some scene. If you run your game as admin, thus run OBS as admin to be able to receive hotkeys while your game is active, you need your companion app run as admin as well, otherwise it would not be able to send a hotkey with a "priority" so high that your admin-running OBS is able to recognize it.
This is all basic Windows security stuff, it doesn't exhibit any flaw in OBS, your game, or the mouse companion app. Best practice is to not ever run any app as admin. The change in OBS 24.0.3 to enable OBS to reserve GPU resources if it is started as admin is a workaround for lost frames with this ugly side effect. I hope, Jim will find a way to enable this feature without the need of running OBS as admin.