The way to stop these distractions is not to set a bunch of rules, but to document things in clear and discoverable ways that people can search to find what they need. No one wants to interrupt; people do that because it's the quickest and easiest way to find an answer. If you make something else the quickest way they'll use that instead.
No, they won't. For example: Tickets are easier to discover, don't suffer from bus-factor=1, act as searchable documentation, can easily be handed over to another team if misrouted, can be queued and prioritized, all those nice things. But people are too lazy to search the ticket system and documentation, then open a ticket and ask incomplete time-wasting questions in chat instead.
It is actually normal for individuals to be lazy, and searching docs is more work (for the asker) than just asking a quick question. This is why rules are necessary, otherwise every asker will just waste someone else's time. It shouldn't just be on the two parties in this interaction to enforce structured communication as a rule, it should also be on the company hierarchy to do so. Because in the end, the whole company will suffer if e.g. the knowledge about fixing problem X died with Bob who always just answered inquiries about problem X in private chat.
