Hello. Based on the attached photos and the information provided, it is most likely that the basil has been affected by a combination of unfavorable factors: the change of environmental conditions (moving), transplanting, a high and constant humidity in the substrate (excessive watering), the installation of pathogens, etc. It is known that a larger pot implies a larger volume of substrate, and thus its thorough drying requires a longer period of time. Therefore, it is important that after transplanting, watering should be carried out with great care, only when the substrate is mostly dry (depending on species requirements and existing conditions). Excessive and/or constant moisture in the substrate favors the development and spread of plant pathogens. Given the current state of the plant, the chances of regeneration are very low.
Indeed, basil can be multiplied by vegetative propagation from plant parts. As a rule, vigorous and healthy plant parts are used for vegetative propagation. In this case, you can consider cutting off some of the stems (2-5 cm above the brown part) and placing them in water or in the substrate for rooting. For propagation it is recommended to use a suitable substrate, such as . After some roots appear, you may consider using a fertilizer such as , by watering at the roots, as mentioned in the product description (to stimulate an optimal development of the roots).
The success of vegetative propagation is not guaranteed.