Applications taking up most of my storage, but I don't have that many applications?

Unfortunately, Apple's diagnostic displays of memory and storage are confusing. They really need to re-engineer that for the modern world.

Right off the bat, you are looking at two different things. One screenshot is memory usage and the other is storage. That's on you.

But Apple isn't innocent here. Apple's "storage" displays are simply atrocious - completely unsuitable, confusing, and outright misinformation. That "248.19" GB value is coming from a Spotlight search of files that it categorizes as "applications". Then it's giving you a list of apps from who knows where. It's all just nonsense.

If I can properly read the background of that screenshot, it seems that you hard drive is totally full? You've used 247.86 GB of 250.69 GB? And of that 247.86 GB, 248.19 GB is applications? Do the math. You can't do the math because it doesn't add up. You've definitely run out of space on your hard drive. In additional to all the other Apple storage misinformation that it normally displays, once you run out of storage like this, it can't even do the math properly. It's a lost cause.

The problem here is that you didn't purchase a computer with the proper configuration. There are lots of people who can get along just fine with a 250 GB hard drive. Not you. You've got at least 3 different versions of R Studio? And calibre? You're not a 250 GB hard drive person. Maybe you're a 500 GB hard drive person, but probably a 1 TB.

So what do you do now? Get yourself an external hard drive and start archiving the files that you want to keep. Delete them off your startup drive. In a couple of days, you'll have more storage available. Then, you can turn on every iCloud option there is to save on storage. Yeah, you'll have to pay for that. I recommend one of those fast little external Samsung SSDs. They are very portable. Just don't get the "Shield" version. The USB port is janky.

Next time, get a Mac with a 1 TB drive.

It is generally a good computer practice to alway keep at least 20% to 25% of the Total Drive Capacity’s as Empty Space.

Allowing the computer to drop below these guidelines may eventually cause unintended consequences such as the Alert it has already presented.

There is Purgeable Space and there is Empty Space.

They are Not one and the same thing

Purgeable Space which is Controlled by the Operating System.

When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur.

The links below will help in identifying what is taking up space on the Internal Drive.

It will also provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

GrandPerspective 

How to delete Time Machine snapshots on your Mac.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shots on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then,  will the Snaps Shots be transferred to the External Drive.

View APFS snapshots in Disk Utility on Mac - Apple Support (CA)

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

If there a Suite of Adobe Applications  used on this computer ?

They may create some very large cache files that can be removed. Though, the Adobe cache files will be recreated as the Applications needs them.

https://helpx.adobe.com/ca/premiere-pro/kb/clear-cache.html

The same clearing of System Cache files can be achieved by booting into Safe Mode

They will be recreated as the System Requires 

Apple's tools aren't going to tell you any of that.

There are some 3rd party storage management tools that will show you your entire hard drive and tell you how much storage is taken in each folder. Just be careful with any "Library" folder. If you delete the wrong file, you could suffer unrecoverable data loss. Don't waste your time with small files. Look for files that are 10+ GB or larger.

But if the computer is 5 years old, it might be a good idea to just backup, erase the hard drive, and reinstall the operating system. The easiest way to restore all of your data is to have all iCloud options enabled. Otherwise, you stand a good chance of restoring whatever problem you had before.

That number isn’t only the size of the application but also the dat created by the apps. Still seems excessive.