I do not envy my unborn 'mixed' son, who will no doubt struggle with the question of belonging to a group with a name that will never quite fit his experiences. His mother has roots in [censored], his father in the [censored]. He therefore might choose to name himself as belonging to either of these groups, but the possibility remains that each of these groups will always label him 'mixed'. Later on he might even come to his parents, asking why he is 'mixed'. I would retort: more diversity is more knowledge and choice, but based on his experiences he might not be convinced. He might opt to embrace only one part of his background, and name himself either '[country name]' or '[country name]' accordingly.
However, nobody is ever quite like the group they would like to belong to. My son could be seen as an outsider, while also feeling slightly out of place in a group regardless. Therefore, naming yourself as part of a group with strict boundaries, either one based on your background or 'mixed' & 'PoC' (Person of Colour), will never satisfy yourself or others.
As his father, I would like him to have a satisfying life. That he feels included and able to share his skills, knowledge and experience with others. Especially others that share his interests, his experience and cultural manners. Yet such cultural manners need not be derived from his parents' background, or his 'mixedness' for that matter.
What matters is not power you derive from recognition, but learning the pros & cons of each group you become part of. In that way you will learn which cultural manners and ideas best fit your life. Then you can form your own group for each experience you have. Because your identity is not defined through one name.