What do you do to get over that lethargic feeling when you finish a great book/show and can't contemplate starting something else?

If it's that good, it's worth spending some time contemplating.

I sit and think about it. Do you feel pressure to always be doing something? Sometimes just breathing is enough.

sometimes just do nothing, literally. meditating I guess.

or go back to something familiar before I'm ready for something new again

Man I feel this question

I just let it be... After completing the last of us or red dead for example, or indeed a great serie or book I just go with it. To put it even more dramatic, it feels like you lost a friend or even a relation. So I just let time heal the wound. After a while I am ready to begin with something new, but that takes some time

Whatever actual responsibilities I haven't been paying attention to because I hyperfocused on something pleasurable but nonproductive, lol.

Read a comfort book/watch comfort show. You know it won't hit as hard, but it'll still be fun.

I solve this by always being in the middle of multiple books at once

You wait and digest. Don't rush into the next thing just because you think you're supposed to.

When I hear about a book that excites me I take a note of it in my note taking app. When I finish my current book I look at my list and pick the most interesting one.

Give it time. You can also look up videos or discussions online to help process it.