Without derailing this into a TERF/ TRA debate, gender identity and cultural identity are not analogous.
However, they have some similarities. Being socialised as a girl differs to being socialised as a boy. Now, you can believe this is based on sexism tropes of what each sex ‘should’ be, or you can believe the gender roles have some grounding in sex-based characteristics - but you can’t deny that as it currently stands, there are differences.
Cultural identity is similar. Perhaps the notion of northerners being friendlier or the Welsh singing better or Londoners being more accepting of others come from an older understanding of each region, but to deny those differences exist is nonsense.
Even as the English language dominates the British Isles, the regional variations in accent and dialect remain. If what you believe about us only getting our culture from American content is true, we would be speaking in American accents and, like, going up at the of every sentence?
Culture is really hard to define - the lack of what you see as an ‘answer’ to you asking what Welsh culture is doesn’t mean it doesn’t exist - it means it’s hard to quantify. It is about food, music, storytelling, community, language, dialect, accent…it all weaves together to form a sense of ‘Welshness’ that is hard to pinpoint but easy to spot.
I’d suggest perhaps before denying the existence of Welsh culture you visit Wales. Perhaps the Welsh ‘expats’ you meet in Scotland commune with you in a way to seek common ground, rather than highlighting their ‘Welshness’.
Going back to Ukraine - they are fighting tooth and nail because they don’t want to be Russian, they want to be Ukrainian. Some insulated person telling them they are virtually Russian anyway so may as well capitulate is beyond offensive.