Postfix: transport_maps SMTP ignores header_checks

I have a working SMTP setup in Postfix

transport_maps = hash:/etc/postfix/transport
smtp_sasl_auth_enable = yes
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd

All is good with the SMTP, however now Postfix ignores the header_checks

header_checks = pcre:/etc/postfix/header_checks

or

smtp_header_checks = pcre:/etc/postfix/header_checks

• Is there a priority of operations, like "use transport and stop"?
• If yes, what could be a way to apply header_checks before transport?

Thank you!

I am not 100% sure why, but when I changed transport map from *:

* relay:[THE_SMTP_HOST]:587

to

specific_email@domain.tld relay:[THE_SMTP_HOST]:587
another_email@domain.tld relay:[THE_SMTP_HOST]:587

the header_checks started working.

(I tried .domain.tld - SMTP stopped working at all)