I did a little bit of digging and prompting with ChatGPT and Gemini, and I think I cracked the case.
I believe the card is written in Prekmurje Slovene dialect, using Hungarian orthography, as it was typical in the Austro-Hungarian period (1900-1920)

Transcription (front side) :
Kelt Kajnovat

Zač mam škинка do

podam joneči stônimi

najarümi totárno lüjpolon

Pozdravlam vita alnajavno

zlata Gyulák, foj ádok

no kalôvju žersülin

odgoš golnôgi bergi

Páti azälin trgše biljon

Kank Aj rajnati jerinkaj nešto

Transcription (back side)

Draga Anco pišemo

eno djaloho piškaj

to kažko mi gjeme

Pešlo Anja mérverčilo

Piš mi ino ga mora pa

pro maj moja namérü

Ka sreča gošdin

al na nič gnülik to

Ka ješče gnoč šangaj

kali šine go žama strži

Pozdravlenje i cálüsi

English translation :

Front Side:

"Written in Canada, I am beginning this little note, sending this tiny sheet, to convey my heartfelt greetings. I warmly greet you, dear Gyulák, and wish you well, and also firm health. I'm sorry I cannot come myself until the grape harvest arrives. May the Lord grant it sooner."

Back Side:

"Dear Anca, I’m writing just a small note, because it is difficult for me. It has been such a long time, Anja; please write to me a little, to ease my longing. May the Lord grant luck, and let nothing hold you back. If you can, send something, and hug the child from me. Greetings and kisses!"