I did build quite a few tanks myself over the years and the tanks are still in use today... Made my fair share of mistakes and sloppy silicon seams... And the majority of them never resulted in a leak except for one tank that I made with too little glass thickness that got ripped apart by a rampant growing emersed Cyprus plant.
It doesn't make me a professional and even if any professional opinion still doesn't give any guarantee, flooding an aquarium in a living room is always exciting, and how well made it can always end up with a wet floor one day for whatever reason. A heavy truck driving by shaking the house? The main cause why tanks start to leak over the years is stress on the seams due to poorly made warped cabinets or crooked floors they stand on and the weight of the tank will warp the glass. Then one day it could become too much stress ripping the seams open or even cracking the glass.
My opinion on your tank based upon my experiences is. If the tank is assembled correctly and the bottom panel is absolutely flat and standing on an absolutely level surface then that 2mm gap floating side panel will not be an issue. The weight is completely supported on the bottom. The side pressure on the panels ain't that great. Considering 10-meter water column results in 1 Bar = 100 000 newtons / square meter. Regardless of the volume dimensions, the tallness of the tank is what counts regarding side pressure if it's absolutely level. You can easily calculate how much pressure it needs to hold if the tank is 60cm tall. That ain't that much.
I can imagine your worries without any experience and it's quite a deal to trust a professional delivering sloppy work on his blue eyes that it is within the safety range. Never the less it is sloppy work that could be prevented... If it were me as a DIY hobby builder I have only myself to blame and still would use it. But regarding a well-paid professional, I personally also would have an issue with accepting silly excuses. This should have been seen before the build and should have been corrected. If they leave you to live on prayer with this, they deserve a very bad review. The least they can do is admit it's sloppy work and give you a partial refund.
I'm afraid you will have to take it as is... Make a back panel from that and forget about it... And if you can't live with the idea, buy another one and it likely will be licking wounds and still forget about it.
Anyway, I've seen much worse made aquariums running without ussies for decades. And also have seen a few cracked open that looked very well made. Buying a tank commes always with guarantee till the door you walk out with it.