set_global_log_level: surprising behavior

[oberstet]

considering

import txaio
txaio.use_twisted()

log = txaio.make_logger()

print('print 1')
log.info('info 1')
log.warn('warn 1')

txaio.start_logging(level='warn')

print('print 2')
log.info('info 2')
log.warn('warn 2')

txaio.set_global_log_level(level='info')

print('print 3')
log.info('info 3')
log.warn('warn 3')

this prints

(cpy39_1) (base) oberstet@intel-nuci7:$ python foo.py 
print 1
2022-05-05T18:26:37+0200 warn 1
2022-05-05T18:26:37+0200 warn 2
2022-05-05T18:26:37+0200 warn 3

I think this should print

...
2022-05-05T18:26:37+0200 warn 2
2022-05-05T18:26:37+0200 print 3
2022-05-05T18:26:37+0200 info 3
2022-05-05T18:26:37+0200 warn 3

Not sure .. how do I use set_global_log_level properly?