Oh, I'm so glad you got good news in the end! That must have been such a stressful week waiting for the follow-up scan.
Honestly, what you went through is more common than you'd think at that early stage. The thing is, a heartbeat at 6 weeks can be really hard to spot on ultrasound, even a few days makes a huge difference in what shows up. A lot of mums I know had similar scares where they couldn't detect anything at first, then went back a week or so later and everything was fine. The key thing doctors look for is whether the embryo is measuring above 7mm without a heartbeat, which would be more concerning, but it sounds like yours was still measuring smaller, so it was genuinely just too early to pick up.
Your HCG levels being in that 4-9k range and not doubling as quickly can definitely be worrying to hear, but that can also be normal depending on when exactly you ovulated and when implantation happened, so the timing matters more than it sounds on first hearing. And the fact that your pregnancy symptoms stayed strong, the sore breasts, tiredness, temperature, those are all good signs your body was doing its thing.
So happy you heard that heartbeat at 6w3d! That's such a relief after the worry. Wishing you a smooth rest of your pregnancy.