From my experience (with Dendrite, not synapse, so keep that in mind), bridges create “fake” users to replicate your contacts on these platform as matrix users, and they are visible on the whole instance by all their users (but you might not be able to talk to them). Also, in puppeted mode (which is what you want to “replace” your app with matrix), only a single user can use the bridge at a time, so the other users cannot use it.
Bridges were not that easy to manage in my case (regarding process management, and ease of config deployment/reproductibility). It was on OpenBSD though, so your mileage may vary.
And still, it leaks all of your contact informations to the other users of the server (like their phone number eventually), so definitely not suited for public instances.
From my experience (with Dendrite, not synapse, so keep that in mind), bridges create “fake” users to replicate your contacts on these platform as matrix users, and they are visible on the whole instance by all their users (but you might not be able to talk to them). Also, in puppeted mode (which is what you want to “replace” your app with matrix), only a single user can use the bridge at a time, so the other users cannot use it.
This is true but if you’re self-hosting it’s not that much bother to add additional copies of a bridge for other users (granted, it’s not ideal).
Bridges were not that easy to manage in my case (regarding process management, and ease of config deployment/reproductibility). It was on OpenBSD though, so your mileage may vary. And still, it leaks all of your contact informations to the other users of the server (like their phone number eventually), so definitely not suited for public instances.