How can I export the "available software to download" to a file?

Open a terminal and type the following:

sudo apt update
apt list --upgradable > ~/downloadable.txt

The list of software available to download will be saved to a file named downloadable.txt in your home folder.

You can ignore the following warning in this case...

WARNING: apt does not have a stable CLI interface. Use with caution in scripts.

Alternatively you can use apt-get

sudo apt-get update

yes no | sudo apt-get dist-upgrade  > ~/upgradeable.txt

You can find the list in your home directory and at the bottom of the file, you'll see something like this:

123 upgraded, 3 newly installed, 0 to remove and 0 not upgraded.
Need to get 180 MB/197 MB of archives.
After this operation, 89,1 MB of additional disk space will be used.

Which can indicate how long the installation of upgrades will take.