I understand that Ukraine is one of the most popular crypto-friendly countries in Europe but it does not mean that the government is not doing its "normal" surveillance job especially with people or organizations suspected of doing illegal things like money laundering, drugs, human trafficking and similar crimes.
You get it totally wrong, where you read that Ukraine is "one of the most popular crypto-friendly countries in Europe"? As far as I know, there are no good laws and regulations that would classify this country as "crypto-friendly". It is possible that you were thinking of Belarus, which has some benefits (0% tax) and plans to build crypto mining farms near the new nuclear plant.
According to what was mentioned in the report, stopping cryptos is impossible, but banning wallets is possible through private keys.
It does not lead to whether they mean central platforms or track transactions and currency bans.
What they can do is just block the accounts on crypto exchanges if they find some suspicious transactions, how they will block your coins in hardware or desktop wallet, maybe by adding your coin/s address to some blacklist?
There is a link from posted article which explains the new law a little better, and by that new law all transaction above $1300 will need to be conducted with obligatory KYC.
As part of the new law, all crypto transactions up to 30,000 Ukrainian hryvnia ($1,300), will reportedly have to be accompanied with Know Your Customer identification and information on the nature of the business relationship between the payer and payee. Additionally, the new law will reportedly come into force on April 24, 2020.