Kath might be able to give you good advice about what to do for optimal results.
What I have learned about celery is that, as long as you keep them moist, they will tolerate everything else in the indoor environment, including crowding, low light and lack of ferts. I have had trays of extras that sat around in ambient light for as much as a year without any complaint, except staying small.
And potted up celery grew nicely in a window that only gets 6 hrs of direct daylight. However, they only grow when I give them liquid ferts. Otherwise, they just stay happily the same size. There seems to be a quick bump in growth whenever they get ferts then nothing.
So I would just treat them as any seedling, but expect to wait awhile for them to get that true leaf on so you can pot them up. Possibly you could speed that up by giving dilute liquid ferts? But I haven't tried that on freshly germinated seedlings, which we sometimes are advised to wait.
I just recently potted up four little celeries that have been neglected pretty severely over the past year - yes they are leftovers from a sixpack from last year! I'm only hoping to get a few leaves and crunches for flavoring our winter meals.
Pretty sure these will bolt immediately if put into cold stress/heat stress or windy conditions that dry them out.