Official bullseye-backports has dino 0.3.

Official pureos repos has 0.3 in octarine.

Add "deb https://repo.pureos.net/pureos octarine main" to /etc/apt/sources.list

and run

$ sudo apt update
$ sudo apt install dino-im/octarine dino-im-common/octarine

For dino master with gtk4 and libadwaita on mobian bookworm follow these steps,
(pureos byzantium gtk4 version is older than what dino master needs so we need
mobian bookworm)

Step 1: Add repo to apt sources:

For mobian bookworm arm64 (Purism Librem 5, Pinephone etc):
  $ wget https://people.debian.org/~praveen/dino/dino-bookworm-arm64.sources
  $ sudo cp dino-bookworm-arm64.sources /etc/apt/sources.list.d/

Step 2: Add repo as trusted:
$ wget https://people.debian.org/~praveen/dino/praveen.key.new.gpg
$ sudo mkdir /usr/local/share/keyrings
$ sudo cp praveen.key.new.gpg /usr/local/share/keyrings

$ sudo apt update
$ apt install dino-im