However I noticed that in their mobile app it became impossible to send or receive the payment without this verification
Actually, they are not wallets they are turning into exchanges not worth having a wallet that asks for KYC. There are lots of issues with blockchain wallets there are many people who were hacked before but blockchain didn't know the reasons and also there are lots of scammers who use blockchain wallets before you can use the search button above to find those threads.
If I were you better not use their wallet and switch to other non-custodial wallets like other said Electrum or build your own airgap or offline wallet.