How do I increment inside an async function safely?

Question

We have a method that splits a Stream into strings based on a delimiter },{. The synchronous version of this works, but the asynchronous version doesn't. I know of race conditions, but not how to fix them.

The important bits:

private static async IAsyncEnumerable<string> SplitReadAsync(TextReader reader, string delimiter, [EnumeratorCancellation] CancellationToken cancellationToken = default)
{
    // read to end if delimiter empty.

    int i = 0;
    char[] cBuffer = new char[1];
    List<char> chars = new();

    while (reader.Peek() >= 0)
    {
        // Read Async
        cancellationToken.ThrowIfCancellationRequested();
        await reader.ReadAsync(cBuffer, cancellationToken);
        char c = cBuffer[0];
        chars.Add(c);

        // If c is not aligned with the delimiter, reset i
        if (c != delimiter[i])
        {
            i = c != delimiter[0] ? 0 : 1;
        }
        // If the delimiter is completed, yield return everything read up to this point.
        else if (++i == delimiter.Length)
        {
            yield return new string(chars.ToArray()[0..^i]);
            chars.Clear();
            i = 0;
        }

        // Logging i never returns higher than 1, But it should reach 2 many times.
    }

    // Return the last thing that was read.
}

I would greatly appreciate an answer, as well as an explanation of what's going on. Microsoft confidently states that await can be used to keep the control flow of your methods clear and readable. "Well obviously threads are a little more complicated than that" I thought to myself, and here I am figuring out if "atomic values" are somehow important. How does one learn to tame this beast that is asynchronous programming: I'd love to know.