you nailed it. the appended query string tells the app what server to look at, and if it’s missing it freaks out. it’s easy to generate on your side - it’s just a base64 encoded string 
E.g., from this viewer link, the query string:
eyJzZXJ2ZXIiOiJodHRwczovL2hlc3RpYS5zcGVja2xlLndvcmtzL2FwaSIsImNhbWVyYSI6eyJ0YXJnZXQiOlstOC42Njg4ODk1OTI1NjcwMywtOS4wMTg4NTkzNzA4MDYzMDcsMC4yNjg4NzI1NDU0NzA3NjYxXSwicG9zaXRpb24iOlsxOS40NjQzODYyMTExMzkzMzUsMTkuMTE0NDE2NDMyOTAwMDU0LDI4LjQwMjE0ODM0OTE3NzEwN10sInJvdGF0aW9uIjpbLTAuNzg1Mzk4MTYzMzk3NDQ4NiwwLjYxNTQ3OTcwODY3MDM4NzYsMi42MTc5OTM4Nzc5OTE0OTQ0XX19
is actually this (via window.atob()):
{"server":"https://hestia.speckle.works/api","camera":{"target":[-8.66888959256703,-9.018859370806307,0.2688725454707661],"position":[19.464386211139335,19.114416432900054,28.402148349177107],"rotation":[-0.7853981633974486,0.6154797086703876,2.6179938779914944]}}
It contains extra stuff for camera rotation, filter by stuff, etc.
so all you need to do to get the links working again is encode just this:
let serverQueryObj = { server: "https://THE SERVER" }
let myLinkUrl = `https://app.speckle.systems/#/${ YOUR STREAM ID }?s=${ window.btoa( JSON.stringify( serverQueryObj ) ) }
Perfect spotting! I didn’t know about your iframe embedding adventures when i made this change. Let me know if it works out!