Eventually I figured it out. Not sure which change mattered most for this but:
in /etc/exim4/update-exim4.conf.conf
dc_eximconfig_configtype='smarthost' dc_smarthost='smtp.englishetc.pl::587'
The ::587 wasn't obvious to me.
in /etc/exim4/passwd.client
# https://poczta.nazwa.pl/ englishetc.pl:bubba@englishetc.pl:passwd smtp.englishetc.pl:bubba@englishetc.pl:passwd ^smtp[0-9]*.englishetc.pl:bubba@englishetc.pl:passwd *.englishetc.pl:bubba@englishetc.pl:passwd