I don't think it's really that important, I'd argue that if you're going to buy a wallet with codebase that could easily be edited it's much better to just buy a wallet from a provider or use your hard disk instead. Cause you're putting yourself at a bigger risk of losing your money to bad actors and hackers. Plus when it comes to "open-source" you can't really do much to verify it besides take the developer's word for it. There's no way for the consumer to confirm whether a program is an open-source until they actually work upon said program.
Don't worry about the trivial details anymore, just make sure you buy a self-custodial wallet and for the most part of your crypto journey, that's going to be enough.
These are not trivial details, on the contrary they are extremely important, this relates directly to the security of your assets and any small mistake can cost you the loss of all your crypto assets.
Buying a self-custodial wallet is not enough. If you mean hard wallets, they also have programs, some of which are closed source and some of which are open source. As for closed source wallets like Ledger, they cannot be trusted, especially after it became clear that the company has access to the seed.
As for wallets that use open source software such as Trezor, we return to the same problem, which is how to make sure that we are downloading the correct software and not the wrong one, because if you download the wrong software, you will lose all your assets.