I agree with that analysis, but it's not clear to me why we don't have similar levels of skepticism about auto-updating desktop apps. Signal in particular uses a third-party software repository, so if it wanted to push a malicious update, it wouldn't even need to sneak it past package maintainers.
Package signing protects you against developers with bad personal security practices, because it makes it harder for a third-party to MITM their apps. But it doesn't do anything I can see to protect you from a developer that turns malicious in the future.
Whether anyone is actually doing that is another question. And there is no technical reason app stores couldn't send a special backdoor-ed build to select list of users under surveillance if government forced them to. (They can target sets of users for staged roll-outs, beta programs, etc.) Which defeats the notion that one person watching can detect it for everybody.
On the other hand, it's possible to do stuff with smart phones at the platform level. Whether through vulnerabilities or some platform capability (updates, etc.), it may be possible to have a backdoor-ed binary that looks to the user like it is the regular binary. That's not a capability that Signal has, but it is a capability that might very well exist.
Regardless of all that, for users who have auto-updates enabled (most users), even if Signal can't silently push a backdoor-ed update, they can unilaterally push one. You could wake up tomorrow with a different version that has a backdoor, so even if you can identify backdoor-ed binaries, you have to turn off updates or verify the binary every time you open the app.
https://wiki.mozilla.org/Security/Binary_Transparency
When you install an app (whether through an app store, or side-loading) the app should state the location online of an append-only log that lists all the releases (with timestamps) for that app. The phone OS could periodically check to see if an upgrade is available, and security researchers could check that the log doesn't contain references to versions which aren't available to the public.
Ideally there should perhaps also be a way for users to anonymously report which version of any app they are using, so that people with particular security concerns could configure their OS to only update an app after, for example, 50% of users have already installed the update.
Telegram is subject to US coercion as much as any US company: both major app stores are US-based, and without app store distribution, a product might as well be dead as far as the masses are concerned.
I would, except it requires a mobile phone number.