Yes, it's custodial since they could reject your transaction and no private key will be given, just like ordinary exchange you access with email password pin code etc.
Yes, the government has designed the wallet in a way that it controls the monetary activities of its citizens using the Bitcoin blockchain as the custodian for that, their monitor and regulate everything through the government's own wallet.
I can understand why El Salvador government did not create a non custodial wallet for their citizens. They want to control citizen transactions if necessary.
I can't speak for El Salvador government but it seems to me that they don't want people to just receive the $30 and go away to forget about bitcoin altogether. They are trying to build the bitcoin economy and encourage people and merchants to start using bitcoin and the $30 acts as the free money to "try things out" instead of just being $30 free money.
In that spirit the 5 transaction would mean the user has at least tried the wallet out and experienced what it means to use bitcoin.
The government did a good thing, bring exposure of Bitcoin and cryptocurrency to their citizens and this effect expands to the world. It is only the good thing I see from El Salvador legal tender.
I hope their citizens will soon realize the importance of non custodial wallet and will choose one to use. Chivo wallet is for their first experience with Bitcoin, first 5 transactions maybe. Later they should use another wallet.
Not your keys, not your coins.
https://notyourkeys.org/