Nuget restore called from C# Script failing

TeamCity Enterprise 2023.11.4 (build 147586)

We are trying to abstract away some of our build steps for C# projects into meta-runners and C# scripts. One of our meta-runners uses the C# script runner to run a script which in turn runs a nuget restore command. Some of the packages that need to be restored are on our own on-prem nuget server which is separate from TeamCity. When just using the built-in nuget restore step, the Nuget Feed Credentials Build Feature works well to authenticate.

However, this new configuration is not working. At the beginning of the nuget restore, we get a FileNotFoundException for System.Runtime. Then, when it's searching for each package, our private nuget feeds can't be accessed, and we get an error saying that CredentialProvider.TeamCity failed.

Starting: "C:\Program Files\dotnet\dotnet.exe" C:\TeamCity\buildAgent\tools\TeamCity.csi.1.0.6\tools\net7.0\any\dotnet-csi.dll @C:\TeamCity\buildAgent\temp\agentTmp\options2.rsp
12:10:04 Starting:  C:\TeamCity\buildAgent\tools\TeamCity.csi.1.0.6\tools\net7.0\any\dotnet-csi.dll @C:\TeamCity\buildAgent\temp\agentTmp\options2.rsp
12:10:04 in directory: C:\TeamCity\buildAgent\work\64743ded94928fc6
12:10:05 JetBrains TeamCity C# 10.0 script runner 1.0.6 net7.0
12:10:06 Command: C:\TeamCity\buildAgent\tools\NuGet.CommandLine.5.11.0\tools\nuget.exe
12:10:06 Command args: restore "C:\TeamCity\buildAgent\work\64743ded94928fc6\MySolution.sln" -NoCache
12:10:06 
12:10:07 MSBuild auto-detection: using msbuild version '17.9.5.7608' from 'C:\Program Files\Microsoft Visual Studio\2022\Professional\MSBuild\Current\bin'.
12:10:09 Restoring NuGet package MyPackage.1.0.0-18.dev.
12:10:09 Restoring NuGet package MyOtherPackage.2.0.0-8.dev.
12:10:09
12:10:09 Unhandled Exception: System.IO.FileNotFoundException: Could not load file or assembly 'System.Runtime, Version=5.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a' or one of its dependencies. The system cannot find the file specified.
...

12:10:11 http://OurNugetServer/index.json: Problem starting the plugin 'C:\TeamCity\buildAgent\plugins\nuget-agent\bin\credential-plugin\net5.0\CredentialProvider.TeamCity.dll'. Plugin 'CredentialProvider.TeamCity' failed within 1.733 seconds with exit code -532462766.

To try to reproduce this, I went as far as logging onto the build agent, installing the TeamCity.csi tool, and running the same C# script with the same arguments that are run from the server. However, the nuget restore works perfectly when I do this. I am at a loss as to what could be going wrong. Any help would be greatly appreciated!