I was a physio for over 30 years, and your doctor friend is right about scans etc in your situation. I also would be very optimistic that you can become pain-free, and that by looking at your muscle imbalances, your back can become stronger throughout your life rather than weaker, and my own experience bears this out. I had back pain in my 20s on and off, which now does not exist at nearly 60, and has not been a problem since my 30s.
I do think most physios focus on muscle imbalance at the expense of general fitness, which is so needed and is possibly why this has hit whilst you are suffering from long coviid. Part of the reason I am still so serious about my general fitness is because I've seen how being extremely fit means I don't get pain from my joints. Strong muscles have hugely protective effects even on arthritic joints (I theoretically have osteoarthritis, but have no effects from it except in my hands).
With the complicating factor of long covid, if the pain persists, I'd ask your GP if you can be referred to a specialist mental health physio. This is not because the pain is all in your mind (although ALL pain, when push comes to shove, is 'all in the mind' since this is where pain is experienced), but because mental health physios have the skills to increase your exercise ability safely without causing a relapse.
Historically, mental health physios end up dealing with lots of chronic pain and chronic fatigue, and although you may happen across one by chance it's generally easier to be referred directly.
The split between mental and physical health is totally false. We are whole bodies - can you imagine if we had 'physical health and liver health' and liver health was thought of by the general public as somehow being nothing to do with the rest of the body, and also carrying a stigma of not beng as 'real' as illness affecting the rest of the body? Yet this is what has happened to the massive excretory and neurological organ that is the brain.
All pain is a total body experience and if it is persistent then it needs a total body approach, and that includes making use of the neurology and hormonal release controlled by the brain.
Having said that, at 6 weeks I wouldn't count your pain as persistent yet (I know it must feel like it, cos back pain affects your body so much). But with the long covid, there are so many factors that need to be taken into account that I'd suggest a referral to a mental health physio sooner rather than later. You can always cancel it if it isn't needed by the time the appointment comes through.
And osteopaths - fine. But stay completely away from chiropractors - total charlatans. Google for Myles Power's YouTube on 'Chiropractic: Quackery Hiding in Plain Sight' and be horrified.