Whenever they're not fighting, machines use their downtime for a variety of activities. A lot of them are directly related to preparing oneself and the environment for the next battle, but there are also things done purely for their entertainment value.
Napping
A big portion of the day is spent asleep or half-asleep. This helps conserving energy.
Storytelling
There are countless stories and legends of varying popularity. Accounts of past battles that the teller was involved in are also very popular.
Decorating the Environment
All available means are used to leave little drawings and notes for others to find. While this can be simple inspirational quotes or the classic "x was here", it is more often than not cynical/obscene jokes or caricatures of unpopular teammembers/leaders.
Getting Drunk
Closely tied to storytelling and usually occurs together. Due to the scarce availability of high-octane fuel, drunk vehicles are not a common sight, though.
Wrecking the Environment
Destroying things is fun.
Shooting Contests
Who can shoot the farthest? Who can hit that tree over there?
Jousting
"That sounds dangerous" - Hunter
Pretend Battles
These can range from very simple to very realistic. Defused training ammunition is most commonly used. Especially in clan territories, more complex simulations with more sophisticated assets like paintball ammunition are the norm.
Cardgames
??????
Tetris
... and similar simple games can be played inside a vehicle's mind. Even though it's dangerous and strongly discouraged, some play these games even during battles.
Blind Arty
A game that is similar to Battleship, but involves a lot more cheating. The players decide the positions of their "team" on a hypothetical map. How many members each team has is agreed on beforehand. The players take turns at guessing the enemy positions by naming a sector of the map. If the sector contains an enemy, it is destroyed. The loser is the player who has all their team members destroyed first. Blind Arty comes with a twist: Both teams are placed on the same map. In order to destroy all enemies, it may therefore be necessary to destroy some of one's own members as well.
Most of the time, the game is played during journeys and without any physical components. It is therefore very easy to cheat, as one can simply move their team members around after placing them. It is in fact assumed by default that the other player is cheating, and part of being good at the game is being able to cheat well.
Blind Arty: Hardcore Mode
Like Blind Arty, but for vehicles made of real steel. Before an actual battle, the team's SPGs study the environment. Once the battle begins, they take turns in shooting blind at certain spots of the battlefield. The SPG who racks up the most kills this way wins.
Note: This variation of the game is generally frowned upon.
Game Shows
Many vehicles with access to radio stations that do them love to listen to various game shows. Usually, they revolve around answering trivia questions, with many trick questions in between. Listeners can apply to be picked as guests - some are just called, while some shows involve the guests being physically present at the radio station. I any case, guests can win awesome prizes.
Audio Dramas
Most major radio channels regularly send various audio dramas. There is a vast variety in genres and plots, and a lot of them have been going on for a long time. Some channels allow listeners to call and suggest what turn the stories should take next. Very few actually allow listeners to send in their own stories.
Popular dramas include Star Track and Lord of the Wings. Every once in a while, the celebrated horror series Silence of the Tankettes receives a sequel, but critics claim that the episodes have become repetitive and only rely on shock value instead of actual dramatic quality.
Singing
Usually this doesn't resemble choir practice, but more of an amateur karaoke evening.
Cleaning Duty
Not a very popular pastime, but it has to be done nevertheless. Team members take turns in clearing their base of used shells, wrecks, and debris.
When I got to Blind Arty, I thought "There are probably some vehicles that play a version of this game with their actual lives" and lo and behold Blind Arty: Hardcore Mode exists. This is probably a good time to say, your worldbuilding is very well structured. The Hummelverse's society is very centered around battling, but it doesn't feel flat at all. In fact, it feels pretty rich in how tanks and other species incorporate it into their daily lives and how it shapes their views of one another and the world. Even if they were to stop fighting, what else could they do? They're warmachines, it's what they were built for. They don't have the resources to sustain themselves any other way, which is evident in the whole factory situation.
That's good to hear! I try my best to keep everything consistent, from the greater societal dynamics down to the daily lives. There's still a lot of things I haven't fully explored yet, but I like to think that I got the most important concepts figured out.
Check out The Hummelverse, the world of AI tanks!
It's good to have everything in order! It saves from having fundamental inconsistencies later.