Or in other words: If I buy ETFs via Degiro set up in Czechia, but I become Irish tax resident and notify Degiro of such tax residency change, and continue buying the ETFs, where are the ETFs actually located tax wise?

Czechia. The transactions (buy and sell, and dividends) occur there through a Czech bank and brokerage, not in Ireland, and unless you transfer that income into an Irish bank, and even then how would the Irish tax authority distinguish between your personal savings and taxable income, it can not be considered taxable by Ireland. And if I recall correctly, Ireland does not tax on worldwide income, only domestic.

Your brokerage is only concerned for compliance on their part and need to know which type of paperwork to issue you. I would personally not see a reason to change my tax information. I would report my internship (work) income in Ireland as normal. And report my capital gains held in Czechia to the Czech Republic as normal. The tax jurisdictions are distinct and the income generated are distinct.

If in the future you decide to bring your Czech money into Ireland, let's say to buy a house or invest, that capital would be categorized as savings, not income, but whatever future returns on that capital generated inside Ireland, will be taxed by Ireland.

Also if it's less than 10,000 euros? No one cares. More than 100,000? Maybe someone will care. If you're really concerned consult a CA in Ireland, typical hourly rate will be 100 euros, but I don't think you'll hear vastly something different.