Manually extracting OpenTelemetry context from golang into a string?

I'm building a simple client server app which I want to trace across the client execution to a server microservice that calls a second server microservice.

Simply speaking, it's not more complicated than CLI -> ServiceA -> ServiceB.

The challenge I'm having is how to serialize the context - most of the docs I've looked at appear to do some form of automated HTTP header injection (e.g. https://opentelemetry.lightstep.com/core-concepts/context-propagation/) , but I do not have access to that. I need to serialize (I think) the context of the trace/span in the client and push it to the server, where I'll rehydrate it. (Mind you, I'd love this to be simpler, but I cannot figure it out).

So the object looks like this (called "job"):

	args := &types.SubmitArgs{
		SerializedOtelContext: serializedOtelContext,
	}

	job := &types.Job{}

	tracer := otel.GetTracerProvider().Tracer("myservice.org")
	_, span := tracer.Start(ctx, "Submitting Job to RPC")
	err := system.JsonRpcMethod(rpcHost, rpcPort, "Submit", args, job)

The function to submit to JsonRpcMethod is here:

func JsonRpcMethod(
	host string,
	port int,
	method string,
	req, res interface{},
) error {
	client, err := rpc.DialHTTP("tcp", fmt.Sprintf("%s:%d", host, port))
	if err != nil {
		return fmt.Errorf("Error in dialing. %s", err)
	}
	return client.Call(fmt.Sprintf("JobServer.%s", method), req, res)
}

And the function that receives it is here:

func (server *JobServer) Submit(args *types.SubmitArgs, reply *types.Job) error {
	//nolint
	job, err := server.RequesterNode.Scheduler.SubmitJob(args.Spec, args.Deal)
	if err != nil {
		return err
	}
	*reply = *job
	return nil
}

My question is how do I, in the receiving function ("Submit" above) extract the trace/span from the sender?

Here is a small program to illustrate the usage. Hope this makes it clear.

package main

import (
	"context"
	"fmt"

	"go.opentelemetry.io/otel/exporters/stdout/stdouttrace"
	"go.opentelemetry.io/otel/propagation"
	sdktrace "go.opentelemetry.io/otel/sdk/trace"
)

func main() {

	// common init
	// You may also want to set them as globals
	exp, _ := stdouttrace.New(stdouttrace.WithPrettyPrint())
	bsp := sdktrace.NewSimpleSpanProcessor(exp) // You should use batch span processor in prod
	tp := sdktrace.NewTracerProvider(
		sdktrace.WithSampler(sdktrace.AlwaysSample()),
		sdktrace.WithSpanProcessor(bsp),
	)

	propgator := propagation.NewCompositeTextMapPropagator(propagation.TraceContext{}, propagation.Baggage{})

	ctx, span := tp.Tracer("foo").Start(context.Background(), "parent-span-name")
	defer span.End()

	// Serialize the context into carrier
	carrier := propagation.MapCarrier{}
	propgator.Inject(ctx, carrier)
	// This carrier is sent accros the process
	fmt.Println(carrier)

	// Extract the context and start new span as child
	// In your receiving function
	parentCtx := propgator.Extract(context.Background(), carrier)
	_, childSpan := tp.Tracer("foo").Start(parentCtx, "child-span-name")
	childSpan.AddEvent("some-dummy-event")
	childSpan.End()
}