However, all wallet software is centralized (whether open source or proprietary).
Is bitcoin core centralized?If we are talking about software, then I think yes. It's currently running on my local PC which is pretty centralized.
The term you're looking for is "self-hosted full node" (if you run Bitcoin Core) or client-side software (for any application which run on your own device).
Decentralised and open source or Closed source and centralised?
There are two main wallet types:- Custodial: you don't own private keys.
- Non custodial: you are the only one owns private keys.
Shared-custodial type of wallet also exist, although it's not popular. The example would be Blockstream Green under option "Multisig Shield".