With Snap and Apt both existing, how do I backup all my apps so that I can restore it on a new machine

For snaps I think a Snapshot is the way to go.

For normal apt(.deb) software packages installed on your machine I think you could try these options:

1. Check your apt archive directory(/var/cache/apt/archives) to see if this contains any .deb file. Those .deb are the software package from the applications you have in your system. If so, copy these .deb file to a USB stick from example, restore them on the new machine and once these files are on the new machine install them using sudo dpkg -i *.deb

2. A second option if the previous step doesn't find anything would be to create the .deb for your current system, on console type:

   sudo apt-get install dpkg-repack
   mkdir repack
   cd repack
   dpkg-repack `dpkg --get-selections | grep install | cut -f1` 
   

The above commands will create the .deb files from your current installed system in the repack directory, from there you could copy these file to an USB stick, then restore them on the new machine, and again, perform an sudo dpkg -i *.deb on the new machine to install these deb applications in there

I am the person who posted this quesiton. Really helpful with the snap save. For the people who are more noob than me (if that is possible), what I've done is

1. I did sudo snap save, this will generate a list of snaps - usually with a preceding ID (Say 12_APP.ZIP, 12_APP2.zip) and this number will increment everytime you take a new snap save.

   You can do mv /var/log/snapd/snapshots/12_*.zip DEST_FOLDER

2. Back it up to cloud or a disk.

3. Move it back to mv 12*.zip /var/log/snapd/snapshots/ on your new machine and you can snap restore 12 on your new machine and TADA!

The synaptic idea by @Organiz Marble was also pretty great. Please do that too.

I've done dpkg --get-selections > package_list. More here - How can I backup my programs/applications, so that after I reinstall a new one, I can still use the backup-ed ones?

(it also backups your PPAs). Thanks, everyone. I hope whoever finds this in the future sees this answer and takes the best of whatever they like :)