When I did dual boot (good riddance) I gave Linux <100 GB and rest to Windows. I had additional storage partitions but in long term they made management harder for me so I mounted Windows partition for additional space.
Here are my recommendations:
Merge "Mint" and "Timeshift" partitions.
Use BTRFS if you can. In rsync mode of timeshift, the disk will hold 2 copies of your current system + changes between snapshots. In BTRFS there will be 1 copy + changes. BTRFS also supports compression.
System wide flatpaks are in /var/lib/flatpak/app. Flatpak installed for one user only are installed somewhere in ~/.var. Keep in mind that home directory is not backed up by default.
If you can, ditch dual boot. If the reason of keeping Windows is MS Office or Adobe apps, you can install them on Wine.
I thought (also most people said) keeping the Backup in same partition as root defeats the purpose of Backup and brings certain inconvenience like can't just delete the partition. Also I don't know if its possible to restore a backup from a partition to the same partition itself.
Use BTRFS if you can.
I'm aware that BTRFS has certain adavantages. But the whole BTRFS is alien to me, as I'm new to Linux. Also I assumed that BTRFS doesn't have enough community support as ext4 is default on Linux and many people just aren't bothered to change it.
If you can, ditch dual boot. If the reason of keeping Windows is MS Office or Adobe apps, you can install them on Wine.
I only use Windows for DaVinci Resolve Free. And for the possibility of requiring Windows exclusive programs in the future as I'm an Engineering Student.
System wide flatpaks are in /var/lib/flatpak/app. Flatpak installed for one user only are installed somewhere in ~/.var. Keep in mind that home directory is not backed up by default.
Btrfs uses snapshots and subvolumes. It is not a traditional partition and can restore to itself.
I think Timeshift is primarily a snapshotting tool for a quick rollback if something breaks. I would not consider it a full backup tool, there are tools that are much more robust and configurable for keeping files safe and elsewhere.
I would recommend using Timeshift. BTRFS mode can create local snapshots and rsync mode can be used to backup to external media. Timeshift can exclude directories based on user preferences.
As the other user says, btrfs is well supported. In fact it is preferable in your case, as it allows you to use transparent compression for the whole system. In addition, btrfs snapshots are also drastically safer and faster.
You can convert it from ext4 to btrfs, but I don't know how well it works. If you are going to do it, I suggest you check it carefully and make a backup.