While your chat is open, nobody can interact with the sister. Another brother cannot start a chat with her and cannot view her photo — the photo chain is frozen for everyone for that period. He is not told that she is in a conversation, either: he sees a neutral "temporarily unavailable" with no explanation of the reason. Until your conversation ends, she is talking to you.
Notifications do not reach her during that time either. Other people's likes, mutuals and photos pile up silently: no push, no Telegram message, no in-app alert. All of it arrives as a single digest only after your chat has ended. The one thing that remains technically possible for others is to send her a like "into the silence": it goes into the queue and will not distract her from talking to you.
As for the feed. By default a sister's profile stays visible to other brothers, but with an "in a conversation" badge and noticeably lower in the results. She does, however, have a "Hide my profile" toggle — it appears on the screen she sees instead of the feed while the chat is running. If she turns it on, she disappears from the profile list altogether. An important nuance: the toggle applies only to the current conversation and resets back to "visible" with every new chat, so it has to be turned on again each time. On his side, a brother can likewise remove busy sisters from his own feed with the "Not in a conversation now" filter.