That sucks.
I'm sorry that your bike was stolen.
If thieves are willing to break into a locked garage, break into a locked and fully enclosed mesh bike parking area then cut two bike locks using power tools: there's not much you can do about it.
If there are lots of bikes in the bike parking area you can make your bike a lower priority target by increasing the number and strength of the locks, and by making the bike itself look less desirable.
Looking at the first picture, it seems the bike parking area door could be easily opened from the inside.
The thieves were able to cut a hole in the door and reach the door release - not the most secure setup.
Also, it's likely that someone let them into the garage - i.e. one of your neighbors.
Just store your bike in your apartment if you can.
bicycles.stackexchange.com/users/24228/Argenti Apparatus
There's nothing you can do if the storage area is not under constant surveillance.
It can take as little as 2 minutes to grind a U-Lock.
The only real solution is to keep your bike in your apartment.
In the meantime, check to know how the thief was able to get in that area ?
did he came via the garage door ?
the front door ?
Did he enter while someone enter or leave without checking ?
Check with your home insurances to see what can be done about that, if the building is responsible in some way.
Anecdotal: When I come in my building, if someone is waiting to be let in, I tell them to wait outside and wait and not come at the same time as I do and if I leave by the garage, I wait until the door is closed before either leaving or going down the ramp.
bicycles.stackexchange.com/users/13517/Max
I lost a few bikes to theft when I was in university.
It stunk.
I took to buying used bikes (probably from bike thieves).
I wrapped the frame tubes of my (otherwise nice) bike in peelable masking tape, then smeared them with grease.
Nobody wanted that ugly bike.
It worked to prevent theft; I kept that one for many years.
bicycles.stackexchange.com/users/27181/O. Jones
Funny enough, the parking garage may actually be less safe than a well-exposed outside location.
When I was commuting between the cities of Hamburg and Berlin
I locked my (500/1000$) bikes at the train stations, sometimes for weeks.
I made sure to detach and lock my front wheel together with the back wheel and frame though, on some steel pole or railing, with a good-quality U lock.
Just one time in two years or so somebody stole my suspended saddle post.
Both stations have their share of homeless and drug-addicted people hanging around; but the places are busy 24/7.
I suppose your average friction saw creates too many sparks at night to go unnoticed in public; but in a parking garage the thieves have all the time in the world.
So try the next intersection next time.
And yes, use a bike which is not a special target.
bicycles.stackexchange.com/users/23487/Peter - Reinstate Monica
There are motion sensors (installed on your bike) and locks that can notify you if your bike is being moved.
I don't have direct experience with them, and they're obviously expensive, so you'll need to decide whether something like that is worth it.
bicycles.stackexchange.com/users/2152/Adam Rice
Check the quality of your locks !
I suspect both to be breakable with a bolt cutter (yes, your u-lock too).
You will learn more here : For owners, a second option is more onerous, but will not benefit only to you.
Install a camera.
Put it high enough to reduce the risk of being destroyed.
Be sure to have access to data even if it is destroyed.
This may even protect the whole garage, not only bikes.
bicycles.stackexchange.com/users/39546/user285259
I park my bike in my building's bicycle room, in the parking garage in the basement.  The garage door can only be opened with a remote fob, and the bicycle room is locked as well.  In the garage, I secure my bike using a U-lock, and a chain lock.  This morning, I came to find a hole in the door, and the two locks cut by what looks like an electrical saw.    What can I do to avoid that should I buy a new bike?
How can I prevent my next bike from being stolen?
bicycles.stackexchange.com
<security><theft>
bicycles.stackexchange.com/questions/57085
bicycles.stackexchange.com/users/39446/Maxime
The safest place to keep your bike is in your house or apartment. However, if this is not possible, there are some things you can do to make your bike less of a target. First, make your bike less desirable than the ones around it. Use a number of locks on your bike that are difficult to break. You can also motion sensors so you are alerted if your bike is being moved. Garages and bike stores should have some sort of surveillance. However, in the end, if thieves are very determined there is little way to stop them. If thieves are willing to cut their way into a locked basement and cut open two locks, no lock is likely to stop them for long. Unlike in a public area, they have time to work without people seeing them. You can use stronger locks, but the only safe solution is to put the bike in your apartment. You can use a camera or motion sensing system to monitor your bike, and try to avoid making your bike an attractive target. Be aware of ways that thieves can gain access to the room. Finally, find out whether your home insurance will cover this loss.
If thieves are willing to cut their way into a locked basement and cut open two locks, no lock is likely to stop them for long. Unlike in a public area, they have time to work without people seeing them. You can use stronger locks, but the only safe solution is to put the bike in your apartment. You can use a camera or motion sensing system to monitor your bike, and try to avoid making your bike an attractive target. Be aware of ways that thieves can gain access to the room.  Find out whether your home insurance will cover this loss.