That sounds pretty similar. My GP didn't mention about post sepsis syndrome but I had looked it up and think that's what mine is too as it started then.
After having sepsis I started having these nasty bouts of shingles starting straight after so I reckon the lowered immune system fighting the sepsis triggered that and both in turn started the CFS symptoms.
I was also low in iron stores and vitamin D so getting those things better helped a bit, then I got another nasty shingles episode on the face / ear and things have been worse since then, also had covid quite badly at the start of the pandemic before the vaccines came out, so it is a right mixture really.
I also have been diagnosed with PTSD (from the sepsis / ops) and have been offered some CBT for that but it is intense CBT and I am just too tired for that right now so I have put it off for now. they said that is fine I can pick it up whenever I feel up to it.
I'm on a cocktail of meds, fluoxetine, olanzapine, gabapentin, co-codomol, all of which help a bit but not a lot.
I am waiting on an appt with the pain clinic (I have adhesions post surgery also causing pain) and that has just come through in a couple of weeks, so will see what they have to say.
I have been on a course with the local CFS clinic and they took all sorts of people with fatigue so that might be an option for you too, if there is anything like that nearby.
Best of luck with it and I hope things improve for us both. My worst fear is getting sepsis again (I had delirium which was really scary)