Crash Log as follows:
java.lang.IncompatibleClassChangeError: class dev.su5ed.sinytra.connector.mod.compat.fieldtypes.RedirectingIdMapper overrides final method net.minecraft.core.IdMapper.m_7942_(I)Ljava/lang/Object;
at java.lang.ClassLoader.defineClass1(Native Method) ~[?:?] {}
at java.lang.ClassLoader.defineClass(ClassLoader.java:1017) ~[?:?] {}
at cpw.mods.cl.ModuleClassLoader.readerToClass(ModuleClassLoader.java:119) ~[securejarhandler-2.1.10.jar:?] {}
at cpw.mods.cl.ModuleClassLoader.lambda$findClass$15(ModuleClassLoader.java:219) ~[securejarhandler-2.1.10.jar:?] {}
at cpw.mods.cl.ModuleClassLoader.loadFromModule(ModuleClassLoader.java:229) ~[securejarhandler-2.1.10.jar:?] {}
at cpw.mods.cl.ModuleClassLoader.findClass(ModuleClassLoader.java:219) ~[securejarhandler-2.1.10.jar:?] {}
at cpw.mods.cl.ModuleClassLoader.loadClass(ModuleClassLoader.java:135) ~[securejarhandler-2.1.10.jar:?] {}
at java.lang.ClassLoader.loadClass(ClassLoader.java:525) ~[?:?] {}
at net.minecraft.client.Minecraft.(Minecraft.java:485) ~[client-1.20.1-20230612.114412-srg.jar%23354!/:?] {re:mixin,pl:accesstransformer:B,pl:runtimedistcleaner:A,re:classloading,pl:accesstransformer:B,pl:mixin:A,pl:runtimedistcleaner:A}
at net.minecraft.client.main.Main.main(Main.java:182) ~[1.20.1-forge-47.1.3.jar:?] {re:mixin,pl:runtimedistcleaner:A,re:classloading,pl:mixin:APP:mixins.emibridge.json:MainEntrypointMixin from mod (unknown),pl:mixin:A,pl:runtimedistcleaner:A}
at jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[?:?] {}
at jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:77) ~[?:?] {}
at jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) ~[?:?] {}
at java.lang.reflect.Method.invoke(Method.java:568) ~[?:?] {}
at net.minecraftforge.fml.loading.targets.CommonLaunchHandler.runTarget(CommonLaunchHandler.java:111) ~[fmlloader-1.20.1-47.1.3.jar:?] {}
at net.minecraftforge.fml.loading.targets.CommonLaunchHandler.clientService(CommonLaunchHandler.java:99) ~[fmlloader-1.20.1-47.1.3.jar:?] {}
at net.minecraftforge.fml.loading.targets.CommonClientLaunchHandler.lambda$makeService$0(CommonClientLaunchHandler.java:25) ~[fmlloader-1.20.1-47.1.3.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandlerDecorator.launch(LaunchServiceHandlerDecorator.java:30) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:53) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:71) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.modlauncher.Launcher.run(Launcher.java:108) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.modlauncher.Launcher.main(Launcher.java:78) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.modlauncher.BootstrapLaunchConsumer.accept(BootstrapLaunchConsumer.java:26) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.modlauncher.BootstrapLaunchConsumer.accept(BootstrapLaunchConsumer.java:23) ~[modlauncher-10.0.9.jar:?] {}
at cpw.mods.bootstraplauncher.BootstrapLauncher.main(BootstrapLauncher.java:141) ~[bootstraplauncher-1.1.2.jar:?] {}

full log?

It works for me when using Sinytra Connecter alongside Alex's Caves Mod. Are you using the wrong Citadel version??
The Connecter beta am using is beta 21 and Forgefied Fabric API is Forgified Fabric API 0.90.4+1.9.28+1.20.1(Latest Version)