A genuine question then, since I've never used Sparrow - how do you use it privately? Can you connect it to your own node directly, or do you need to run an Electrum server first?
You can connect your Sparrow wallet directly to Bitcoin Core, and this is one of the main reasons why I consider it a good alternative to Wasabi wallet (with which it is also possible to connect to Bitcoin Core directly), especially when it comes to non-mobile clients with in-built CoinJoin functionality, of which there are unfortunately very few on the market.
If I'm already running a Samourai Dojo server, can it connect to that instead?
I have no idea. I only know that there are three options Public Electrum, Bitcoin Core and Private Electrum. According to
this documentation, Samourai Dojo is using Bitcoin Core as a base layer to connect to Bitcoin network.
Other than platform availability, what are the advantages of Sparrow?
In-built CoinJoin, BIP47, nice UI, easy-to-use with air gapped hardware wallets.