(everyone's different, so adjust to taste)

• Check for 'comfort' entertainment: I often reread a few books I've had since being a teenager (known comfort) or trashy fanfiction (new but I don't feel bad about not paying full attention) to provide enough distraction to rest in these situations.
• Depending on the relational dynamics, either offer to screen comms or suggest do not disturb for notifications with checks at specific times of day. Even people wanting to support can be a huge drain.
• Avoid the news if possible. Stuff out there can be important and meaningful, but sometimes we don't have the emotional bandwidth to deal with it.