All of those tools have ways to export their wallet‘s xpub – which can then be imported to BTCPay Server as a watch-only onchain wallet. I think this setup is cool enough and I was overcomplicating it by wanting to share the hot wallet.
Direct benefit: your store’s funds are immediately available for opening Lightning channels or coinjoining – I think the latter is pretty nice, when you use JoinMarket‘s mixdepth 0 xpub. nostr:note19zxxd0zc7lgl4evwy6n57nlj6e7k2su8ph50ngcdrshr0k2knzjqnz6vev