Great question! There are different ways to figure out if you own your private keys or not. Before we discuss, let's clarify that a non-custodial wallet will always expect you to back up your private keys. Some wallets make this mandatory, while others leave it optional.
When you set up your wallet and were asked to write down a "seed phrase" (12 or 24 words), then you own your private keys! These words are not the private keys themselves but are used to derive the private keys automatically in your wallet, allowing it to generate the private keys needed to sign transactions. You can also check the wallet’s options or settings for features like "export private keys" or "show seed phrase." If you only have a username and password, it is likely a custodial wallet where the company manages the keys for you.
There are exceptions, of course. Some software wallets use a different system than the seed phrase, and you might possess the private keys without owning a seed phrase. For example, Edge Crypto Wallet uses a combination of username and password to create wallets and private keys in the background.
If you are still unsure whether your wallet is custodial or non-custodial, you can search online using terms like "wallet review," "non-custodial," and "custodial." This will help you find information about the wallet’s custodianship status.
Some older wallets may not use the BIP39 standard (which uses seed phrases) but might offer options to back up private keys for individual addresses used.