Python 3, 81 bytes

import re L=[*map(len,re.findall("[A-Za-z]+",input()))] print(max(L,key=L.count)) 

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Finds all runs of letters using regex, collects a list of the lengths of those runs, and prints the item with the maximum frequency in the list.

Python 3.8, 81 75 bytes

Thanks to Mukundan314 for 5 bytes and ovs for another 1 byte

lambda S:max(L:=[*map(len,re.findall("[a-z]+",S,2))],key=L.count) import re 

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Anonymous function: Finds all runs of letters using regex, collects a list of the lengths of those runs, and prints the item with the maximum frequency in the list.