Last things first: on my phone I only run syncthing "on demand", so I can't actually answer your question. Maybe someone else can chime in? From the little I've brushed up against the issue you're referring to, I think there's a way to have it not get killed, but it seems like it might be a little bit of a hassle.

On the transfer, here is what I could dig up:

The github issue about it was deleted, but archive.org has copies: https://web.archive.org/web/20251215062049/https://github.co...

HN discussion of same (with another link to the syncthing forum): https://news.ycombinator.com/item?id=46184730

Lobsters discussion: https://lobste.rs/s/urbcpw/potential_security_breach_syncthi...

(and here is the announcement that the official android syncthing app was being discontinued: https://forum.syncthing.net/t/discontinuing-syncthing-androi...)

No shortage of reading if you have the time! I'm quite happy to be running just the "standard" package (although, yeah, I should've pointed out that I don't run in continuously on my phone...)