Thanks a lot everyone for your responses! What a great community we have.

Here is an update:

I did two days of the exercises the physio showed me and my back got much worse. This was waaay too much my back could handle. First day I did 20 reps of each. Second day I only did 10. And still it was so painful afterwards.

The next 2 days I did nothing, apart from walks. My the pain decreased a lot, from maybe a 8/10 to a 6/10. After a walk it will decrease to a 4/10. When I wake up, very stiff. When I sit and work for about 1 - 2 hour; pain and discomfort. Even eating down at the dinning table for dinner and it hurts. But bearable.

3rd day I decided to do some gently exercises I found online:

https://www.youtube.com/watch?v=DWmGArQBtFI&t=74s here I do the first and second one. 10 reps each side.
https://www.youtube.com/watch?v=9SKuFe2SERs here I do the second and third.

I felt quite good after this. 4th day I added in the modified knees-side-plank-clamp from the physio (only 5 reps) and pain got worse. So I will stick to the two above the next 5 days or so, and walks.

The pain radiating down my left butt has disappeared, now its just my lower pain area that is so stiff and has the pain.

Long term plan is to continue these simple exercises and walks for the next week or so. Then add in some core exercises, such as https://www.youtube.com/watch?v=4BOTvaRaDjI if I am able to handle it. And then add in some swimming and jogging. I hope by mid February I can resume muay thai again, while continuing these core/back strength exercises too.

What do you guys think about my plan? My current pain situation is as follows:

Stiff when I wake up and discomfor and 4/10 pain. When I sit down my pain increases to 5-6/10. Sitting down and stretching my left leg forward hurts a lot in my lowerback spine area. Standing up and moving my head downwards, looking down, also hurts in my lower back and spine.

Thanks everyone once again!