Refresh Workaround for Sidestore+LC iOS 26.4+
Just so everyone currently on iOS 26.4+ that is having issues refreshing apps knows, there is now a successful workaround to refreshing apps locally on device.

User LamDoHoang on github posted this solution and it is working for me.

connect to VPN Super IKEv2
Connect to LocalDev VPN
refresh your apps
VPN super can be found on the app store labelled VPN super Unlimited Proxy, it is free as of writing this.