Clearing storage on Macbook Air not registering

I've been trying to back up my iPhone to my Macbook Air but getting a message saying there's not enough storage on the computer.

I've cleaned out a lot of files and moved things to the cloud and now under the About This Mac - Storage Section it's saying I've got over 300GB of storage which is more than enough to back up the phone.

However, when I go into the System Report section (also under About this Mac) it doesn't seem to have registered this and is still saying I only have around 46GB of available storage which is what it was saying when I first started clearing it.

Any thoughts or suggestions as to why this is and what to do about it.