cursors_example.py

import arcpy

fc1 = 'buildings'
fc2 = 'buildings_1'
fields1 = ['osm_id', 'type']
fields2 = ['osm_id', 'test']
libraries = []

# loop through each row in fc1 and add the osm_id to the libraries list
with arcpy.da.SearchCursor(fc1, fields1) as search_cursor:
    for row in search_cursor:
        if row[1] == 'library':
            # print(u'{0}, {1}'.format(row[0], row[1]))
            libraries.append(row[1])

# loop through each row in fc2 and update the 'test' field if the corresponding osm_id is in the libraries list
with arcpy.da.UpdateCursor(fc2, fields2) as update_cursor:
    for row in update_cursor:
        if row[0] in libraries:
            row[1] = 'this is a library'
            
        update_cursor.updateRow(row)