Catapults exist and are used
But they make awful anti-personnel weapons
Their ranges are very limited
In my country (Russian Federation), catapults are usually given very strong stats. They usually take down anyone with a direct hit, they take down castles quite quickly. But safety guidelines make ranges very small, catapults are extremely inaccurate, and, even with a successful hit, you are only taking down one person.
Anti-personnel weapons should be more easily aimed than a catapult. Consider ballistae (giant crossbows) or cannons. I have personally used a cannon, read below about its limitations.
Siege weaponry is clumsy to transport
Your catapult or whatever mechanism of choice will take a lot of space in your car. When the even starts, it will greatly slow you down on a march and make you unable to escape any enemies without leaving the siege weapon behind: for example, if you meet a monster that you can't beat or a warband that you don't want to engage. You will just get tired of dragging a heavy thing all day long unless you have a lot of people to drag it.
Theoretically, you can use a catapult to fire over a wall, but that's not practical unless you can accurately measure distances and have a spotter helping you to adjust your fire. I haven't seen it done successfully yet.
Large-scale battles (several hundred participants
Siege weapons can be used in large-scale battles, but limited ranges take away all the fun. You can easily get charged before you are given a chance to fire, often requiring special rules to be developed so that the said weapons can be at least somewhat effective. For example, Warhammer LARP in 2018 gave the shooters 3 minutes to safely fire at the enemy formation before the infantry was allowed to even start moving.
Some things are better killed with siege mechanisms
On the other hand, siege weapons are very effective at taking down castle gates: that's what they were usually used historically for. In my area, catapults usually deal a lot more damage against city gates, which means less time spent firing after you establish your aim. If you plan to be a part of a large army and besiege castles, you will need siege weapons, and a catapult may be your weapon of choice.
Some monsters (e.g. Warhammer Stormvermin) are most easily taken down with siege weapons when magic is not available.
So don't bother if it's your first LARP
As you can see, catapults and the like are very niche weapons. They are good at taking down something that can't move while you are covered by friendly infantry. They are very bed at firing at anything moving fast.
If it's your first time, relax and better be a roaming party seeking for adventures. If you plan for something too niche and it doesn't work, you will be greatly disappointed.
Only bother taking them to an event if you know what you are doing and plan to besiege someone or to fight monsters who can only be taken down by siege weaponry.