In this context,
'People you are social distancing with'
is short for
'People you are practicing social distancing with'.
The noun phrase 'social distancing' is now being used as a verb, rather than as a direct object of 'practice'.
That is, 'to practice social distancing' (Verb + Direct Object Phrase) has been shortened to 'socially distancing'.
Here, 'practice' means 'to carry out or perform (a particular activity, method, or custom) habitually or regularly' (Lexico).
The workbook wants the kid to draw a picture of the people she/he is habitually or regularly (practicing) social distancing with as a way to recall these days, people, and activity in the future--and especially the people with whom she/he has been (practicing) social distancing.
This means you make a drawing in the available space those people with whom you are practicing social distancing: it means those people in your life with whom you are together during this ongoing Covid19 situation. It means people close to you during this crisis, literally, as in you and they are part of your family or friends with whom you are doing this activity; not people you are staying away from--although if someone in your family did have the virus or test positive, it would not be wrong to include them in the picture. This is only an interpretation and not necessarily conclusive, the preposition with tends toward being close, not being separated.
For 'social distance' as a verb, see (MacMillan), whose definition happens to be 'to practise social distancing', using the UK spelling of the verb 'practice/practise'.