Unfortunately a lot of Reddit communities have not transferred over to Lemmy so I have to use Reddit logged out. But now the comments aren't loading anymore...
I don't know if Lemmy will search the entire fediverse, like kbin does. Be sure to check kbin instances as well as Lemmy. I have found some communities that migrated only to kbin.
If you search on either a lemmy or kbin instances, it should be able to find comments/threads on communities/magazines on Threadiverse (lemmy/kbin) instances that (a) are federated and either are local to the instance or (b) have a local user who subscribes to the community/magazine in question.
Neither will typically search the entire Threadiverse, because they only search content that they have a copy of locally, and no one server intrinsically gets a copy of all content on the Threadiverse.
I don't know how kbin deals with searching for comments off Mastodon. That's a good question. You can set a magazine to include comments with given hashtags, and I am wondering if basically it sees the content on local magazines or remote magazines with the same rule above as having a local user who subscribes to such a magazine.
I'd say that Reddit's been pretty reliable for some years.
When they were scaling up, there were points where it was a lot flakier.
I think that that part of it was more testing before stuff went to production. Also, they have a lot of publicly-visible monitoring stuff now that didn't exist when it was young, and I'm pretty sure that they have someone who gets notified immediately if one of various things breaks, since they started putting up a message quickly when something broke with a quick summary and giving an ETA on a fix; their time to get stuff fixed also fell off. The early days, I remember things not infrequently breaking for a day or so.
If they did a door some sort of a ban that includes seeing comments, it would apply to any device they've connected to your account regardless of if you're logged in or not.
I've tried on my phone browser, my computer browser, a different browser on my computer and incognito mode. All of them won't let me see any comments.
But then I try on my brother's computer which I've never used, and it works fine