FWIW, here is a peekable stream over a non-seekable one, optimized for just one byte ahead:

public class OneBytePeekableStream : Stream
{
    private readonly bool _disposeStreamOnDispose;
    private readonly Stream _stream;
    private int _buffer; // byte or -1
    private int _bufferLength; // 0 or 1

    public OneBytePeekableStream(Stream stream, bool disposeStreamOnDispose)
    {
        if (stream == null)
            throw new ArgumentNullException(nameof(stream));
            
        _stream = stream;
        _disposeStreamOnDispose = disposeStreamOnDispose;
    }

    public override long Length => _stream.Length;
    public override bool CanRead => _stream.CanRead;
    public override bool CanSeek => _stream.CanSeek;
    public override bool CanWrite => _stream.CanWrite;
    public override bool CanTimeout => _stream.CanTimeout;
    public override int ReadTimeout { get => _stream.ReadTimeout; set => _stream.ReadTimeout = value; }
    public override int WriteTimeout { get => _stream.WriteTimeout; set => _stream.WriteTimeout = value; }
    public override long Position { get => _stream.Position - _bufferLength; set { _stream.Position = value; _bufferLength = 0; } }

    public override int Read(byte[] buffer, int offset, int count)
    {
        if (buffer == null)
            throw new ArgumentNullException(nameof(buffer));

        if (offset < 0)
            throw new ArgumentOutOfRangeException(nameof(offset));

        if (count < 0)
            throw new ArgumentOutOfRangeException(nameof(count));

        if (buffer.Length - offset < count)
            throw new ArgumentOutOfRangeException(nameof(count));

        if (count == 0)
            return 0;

        if (_bufferLength == 0)
            return _stream.Read(buffer, offset, count);

        if (_buffer < 0)
            return 0;

        _bufferLength = 0;
        buffer[offset] = (byte)_buffer;
        if (count == 1)
            return count;

        var read = _stream.Read(buffer, offset + 1, count - 1);
        return read + 1;
    }

    // this is the sole reason of this class
    // returns -1 is stream is EOF
    public virtual int PeekByte()
    {
        if (_bufferLength > 0)
            return _buffer;

        _buffer = _stream.ReadByte();
        _bufferLength = 1;
        return _buffer;
    }

    public override int ReadByte()
    {
        if (_bufferLength == 0)
            return _stream.ReadByte();

        if (_buffer < 0)
            return -1;

        _bufferLength = 0;
        return _buffer;
    }

    public override long Seek(long offset, SeekOrigin origin)
    {
        var ret = _stream.Seek(offset, origin);
        _bufferLength = 0;
        return ret;
    }

    public override void Flush() => _stream.Flush();
    public override void SetLength(long value) => _stream.SetLength(value);
    public override void WriteByte(byte value) => _stream.WriteByte(value);
    public override void Write(byte[] buffer, int offset, int count) => _stream.Write(buffer, offset, count);

    protected override void Dispose(bool disposing)
    {
        if (disposing)
        {
            if (_disposeStreamOnDispose)
            {
                _stream.Dispose();
            }
        }

        base.Dispose(disposing);
    }
}