If you want to use split, you can use an alternation to either capture the content that you want to keep after the split in group 1, or match where you want to split on.
In the result, remove the empty strings from the result.
([[^][]*])
Capture group 1, capture from an opening till closing square bracket
|
Or
[-+*/&,^%]
Match any of the listed characters you want to split on
Regex demo | Python demo
Example
import re
s="[var1]+[v/ar/2]^var3/var4"
result = list(filter(None, re.split(r"([[^][]*])|[-+*/&,^%]", s)))
print(result)
Output
['[var1]', '[v/ar/2]', 'var3', 'var4']
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