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Since it lacks a final 'h', I think it's most likely a simplification of Azerbaijani "Qasımzadə". This form is non-standard in Azerbaijan, but simplified forms are frequently used even by native speakers outside of Azerbaijan (and occasionally from within as well). Since the bearer you mentioned was a Russian speaker, I think this is the most likely scenario in their case. "Gasimzade" would be the most common simplified form, but variation is fairly common.

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This spelling can also be an alternative romanisation of Qasemzadeh in Persian. Persian (outside of Academic resources) typically does not use a standardised Latin orthography and, as an abjad, it usually omits vowels so there is a lot of ambiguity on how to transliterate it. Thus, most names in Persian have at least 3-5 variations, but that can easily go up to a dozen on some of the longer ones.

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If you go to https://forebears.io/surnames/qasimzade and navigate to "Phonetically Similar Names", most of the results are simply spelling variants in Azerbaijan and/or Iran (though some may be typos or genuinely distinct names).