I recently flew QF2 LHR-SYD and QF9 MEL-LHR (with a domestic connection SYD-MEL prior);

At LHR before I was allowed to enter the check in area, a member of ground staff had a checklist and was checking that:
- I was booked to fly that day (inc passport check)
- I had a vaccination certificate
- I had completed that digital locator / arrival form which Australia had instigated the week I was flying
- I had a negative test result (I had a PCR test as I wanted it to cover entry to both Italy 2 days prior where my ticket originated, as well as Australia)

I everything printed out (except I'd missed there was a summary page for the arrival doc that I needed to log in / dig out and show on my phone) and it was pretty painless from there, once allowed into the check in area I had my boarding pass issued and was on my way.

I would imagine if you weren't able to provide a negative test result that you could/would show the QF medical exemption form you linked to and you'd be ok, and I imagine they'd be very happy with MedicSpot (that's a useful service that I may need to use myself at some point- so thanks!)

On the return earlier this month I had to show my vaccination and UK PLF only, which I did on my phone.

All of the checks were quite casual/not even the slightest bit thorough. I am a dual UK/AU national so didn't have to speak to an immigration officer at arrivals in either direction, who I imagine may have wanted to check things in more detail...

If I were in your position I would get the recovery certificate filled in (using a service like the one you linked to), and I'd be making sure I had a healthy stock of LFTs at hand to do your own surveillance over the next couple of weeks. That way you should know whether a paid RAT is likely to show positive on the day you take it. (I'd not risk paying for a PCR test <3 weeks after testing positive - in fact from memory they might not admit you to a test centre if you've had a recent positive result?)

My partner's on day 9 and today's the first day his LFT/RAT is showing even a slight lightness in the "T" line. His dad had it a few weeks ago and was testing positive up to day 13, but hasn't had any positive tests since.

I would spend the next week or so getting as much rest as possible and focusing on recovery, hopefully your symptoms are mild and pass quickly and you're back on your feet and ready to travel before you know it.