It seems that using a multisig wallet with a pruned Bitcoin Core node could be a good incremental improvement of securing assets vs. storing funds on an exchange or on a single seed hardware wallet.
* When you have your bitcoins in an exchange (or any custodial wallet for that matter) you have zero security and zero privacy because the third party controls your money not you.
* Security of a multi-sig versus a single sig is not that different as long as one person is the owner of all keys. Multi-sig scheme is useful for multiple parties or at least if you are both creating and storing the keys separately otherwise it is the same as a single-sig.
* Security of running a full node versus a light client is obviously higher. Being pruned doesn't change the fact that the node is still a full node, it just doesn't store the historical blocks that are too old.
* Security of an offline storage is higher than a hardware wallet and is higher than an online wallet including a full node that is connected to the internet (operating on an online computer).
[I'm not familiar with Specter to comment on it]
Chain analysis companies are able to gather information from non-self-hosted nodes and tie it to personal information.
Chain analyzers are analyzing the "chain" not the network although that is a possibility but it is a much harder thing to do. However, you do gain additional privacy when running your clients through TOR since it prevents other kinds of attack such as packet sniffing.
