Prepaid gift cards can be purchased with cash, but using prepaid gift cards for transactions will typically require providing personal information due to KYC/AML. Basically, transactions are monitored by third-party payment processors to prevent funding terrorism, money laundering, and other financial crime. Since prepaid gift cards are issued by regulated financial institutions, they are subject to increased scrutiny compared to cash in circulation.
Anonymity is a complex subject that cannot be technically guaranteed:
Instead, to efficiently move forward with the discussion, it is more effective for me to state that there is always a risk of deanonymization that will continue to grow as time goes on, because anonymity as a digital concept is under constant and significant threat of erosion by various actors/agents. Even if you stay informed and/or adopt complete behavioural changes, what may be considered safe for you now may be considered unsafe for you later.