Logistically, you can't go out as much as you used to but you could still one or twice a month?
Could you have the childcare to attend a class or a course in an evening as it sounds like you like socialising?
Could you look back to when you were a teenager and see what hobbies you used to enjoy? Some or even many may not interest you now but you might still be into something from back then.
Do you want to learn something like a language, instrument or skill?
I think would make a list of when I'm free and for how long, could be 20 minutes could be 2 hours, look at your calendar and mark all the free time.
Then I would look at whether it's important to you to do it around people or alone, or maybe a mix of both.
Then I would look at budget. Some things are free like walking groups or park run or language exchange or volunteering.
Then I would make a list of all the things I would like to learn or be able to say I can do or have achieved, and start making baby steps towards them. And if it's not fun, cross it and move on to something else.
You might like to make a 'brain map' of what identity means to you in general terms and then what your current identity is and then what you would like your identity to be, what do you think it's lacking (creativity, fun, social connections,... whatever!), which values or hobbies or skills do you wish to have for your name? What sort of people would you like to meet or life do you want to lead and what kind of interests are conducive to leading that life and meeting such people? It's thinking what tribe do you want to belong to, what sort of life style and values do you want in your life?
Come at this from a place of excitement for this new adventure of discovering new interests and focusing on yourself, this is something for you, rather than I have to find something because my life is so boring and I have no identity. Frame it as an exciting opportunity that can take you anywhere.