It looks like in-process Azure Function Model requires the package System.Text.Json 6.0 version as per this github issue but this version can’t be used in .NET8 in-process function, you need to use 8.0 version or above.

So, you can use System.Text.Json in .NET6 in-process function model or else use Newtonsoft.Json in .NET8 in-process function model.

If you are comfortable to move to isolated function model then System.Text.Json package works perfectly fine for .NET8 isolated model.

I have created an isolated function model with given code in it.

using Microsoft.AspNetCore.Http;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Azure.Functions.Worker;
using Microsoft.Extensions.Logging;
using System.Text.Json;

namespace FunctionApp2
{
    public class Function1
    {
        private readonly ILogger<Function1> _logger;

        public Function1(ILogger<Function1> logger)
        {
            _logger = logger;
        }

        [Function("Function1")]
        public async Task<IActionResult> Run([HttpTrigger(AuthorizationLevel.Anonymous, "get", "post")] HttpRequest req)
        {
            string requestBody = await new StreamReader(req.Body).ReadToEndAsync();
            dynamic data = JsonSerializer.Deserialize<JsonElement>(requestBody);

            string name = null;
            if (data.TryGetProperty("name", out JsonElement nameElement))
            {
                name = nameElement.GetString();
            }

            return new OkObjectResult($"Welcome to Azure Functions, {name}!");
        }
    }
}

.csproj –

<Project Sdk="Microsoft.NET.Sdk">
  <PropertyGroup>
    <TargetFramework>net8.0</TargetFramework>
    <AzureFunctionsVersion>v4</AzureFunctionsVersion>
    <OutputType>Exe</OutputType>
    <ImplicitUsings>enable</ImplicitUsings>
    <Nullable>enable</Nullable>
  </PropertyGroup>
  <ItemGroup>
    <FrameworkReference Include="Microsoft.AspNetCore.App" />
    <PackageReference Include="Microsoft.Azure.Functions.Worker" Version="1.23.0" />
    <PackageReference Include="Microsoft.Azure.Functions.Worker.Extensions.Http" Version="3.2.0" />
    <PackageReference Include="Microsoft.Azure.Functions.Worker.Extensions.Http.AspNetCore" Version="1.3.2" />
    <PackageReference Include="Microsoft.Azure.Functions.Worker.Sdk" Version="1.17.4" />
    <PackageReference Include="Microsoft.ApplicationInsights.WorkerService" Version="2.22.0" />
    <PackageReference Include="Microsoft.Azure.Functions.Worker.ApplicationInsights" Version="1.4.0" />
    <PackageReference Include="System.Text.Json" Version="8.0.4" />
  </ItemGroup>
  <ItemGroup>
    <None Update="host.json">
      <CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
    </None>
    <None Update="local.settings.json">
      <CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
      <CopyToPublishDirectory>Never</CopyToPublishDirectory>
    </None>
  </ItemGroup>
  <ItemGroup>
    <Using Include="System.Threading.ExecutionContext" Alias="ExecutionContext" />
  </ItemGroup>
</Project>

It works locally as well as in function app.