Screen mirroring to extend screen of MacMini+Studio Display to 2019 iMac

I'm using Screen Mirroring to extend (not mirror) my mini M4's studio display screen onto a 2019 iMac. Both are connected by ethernet to the same network. Got a couple of issues and was wondering if anyone knew anything. 1. When I first extend the screen my mini's sound output is changed to the 'iMac Airplay' output. I have to open Sound preferences and change it back to 'Studio Display speakers USB' every time I start Mirroring. Can I prevent this? 2. The resolution options for the iMac are all over the place. It offers several resolutions but they are all the wrong aspect ratio or the wrong scaling (the options are 3840 x 2160, 2880 x 1620 (low res), 1920 x 1080 (default), 1280 x 720). If I enable 'show all resolutions' I can select 2560 x 1440 (low res) which is the correct scaling and aspect ratio but only half the iMac's native resolution. This is the setting I've been using. It's not terrible, just slightly blurry. The lag is noticeable but not a show-stopper. I've seen some mentions online of using a thunderbolt cable to improve Mirroring somehow. It's not very clear if it will improve the lag or the available resolutions. Ideally I'd like to achieve 2560 x 1440 (high res), but I'd settle for less lag. I've tried connecting the two macs with a couple of different thunderbolt cables but I can't see any differences. The available resolutions don't change and the lag is the same. Do I have to do something special to make it use the cable?