It’s reproducible if the checksums match, otherwise it would be useless. The point is trusting a process that from time to time anyone can check by reproducing the build and comparing the checksums. If someone (Logseq devs or GitHub) tries to distribute altered builds it would be found out. Indeed this is why Telegram implements reproducible builds, for example.
I asked them to public it and in the end they made it available, so Logseq is fully FOSS client-side 
Yes, but more as an indication that the upstream devs recognize that FlatHub app as an officially supported way to install their app.
When it comes to Logseq, there is always GitHub as gatekeeper and only reproducible builds can guarantee you are running the actual public code:
(Logseq) -> [GitHub Actions] -> users
(Logseq) -> (FlatHub) -> [GitHub Actions] -> users
(...) = open/public
[...] = black box
As I said, many apps on FlatHub have reproducible builds and, if I remember correctly, Logseq too.