I tried to remove it manually but it keeps growing back -blue arrow -weed to get rid of -red arrows -hen and chicks+their flowers(dying flowers) -green arrow -some ground cover that should not be there
The best, but not easiest, way to remove the wood sorrel is to dig up a shovelful of the area - sempervivum (hens and chicks), wood sorrel, and anything else that's growing there. Take the shovelful of soil to a separate area, remove the sempervivums (just keep the roots, not the soil) and set aside, then remove the weeds and discard them. Do this for the entire area, then replace the now weed-free soil and replant the sempervivums. It's essential that you get the entire root system of the wood sorrel or it will return.
Note: the hens and chicks that have bloomed will die, so there's no need to replant them.
Your photo shows a lot of Oxalis corniculata L. which I grow as an edible plant. Often, they perform better under poor conditions in the lack of competition from larger plants.
Hens and chicks (Sempervivum tectorum) on the other hand grows well under challenging conditions like among hot and dry stones almost without any soil.
To get rid of annoying weed you will have to arrange an alpine garden, which only allows your alpine plants to survive.
I have Oxalis corniculata (creeping woodsorrel) on my allotment. It's a bit of a nuisance. If you can't spot treat the woodsorrel with Roundup, remove and temporarily transplant the sempervivums you want to keep. Spray the woodsorrel with Roundup (carefully - follow all instructions). Wait at least seven days before replanting the sempervivum. Water as necessary until established. Hand weed or spot treat any reappearing woodsorrel.