While the installer uses FAT32 for boot, an install must be a Linux partition, default is ext4.
But if installing to an external flash drive or SSD, best to use gpt partitioning & have ESP - efi system partition and the LInux partition on external drive. Default typically is to to install boot loader (grub) to first drive or internal drive. That is why we often suggest disconnecting all other drives. Some UEFI allow turning off/disabling a drive in UEFI settings.
If you have ESP on external drive, then you can boot it just like you boot live installer on any system using a drive entry by label/brand or drive. If always using with one system then you typically have an "ubuntu" entry.
My external M.2 SSD, internal NVMe drive is now just Windows. I do use a data partition and keep / (root) a bit smaller, but new users probably should just have /, unless drive is very large.
Code:
fred@m2-noble:~$ lsblkt
MODEL NAME FSTYPE SIZE FSUSED LABEL PARTLABEL MOUNTPOIN UUID
Samsung SSD 850 EVO M.2 250GB sda 232.9G
├─sda1 vfat 510M 10.4M EFI System Partition /boot/efi A02D-F0F6
├─sda2 vfat 5.9G m2_fat m2_fat 4738-7B8C
├─sda3 ext4 35.2G 9.7G m2-noble m2_noble / 09a68bbd-3d26-4630-b18e-7c687761aa36
└─sda5 ext4 127.4G 22.6G m2_data m2_data /mnt/data 0c374965-53c6-437c-a2ad-f0508486f9d5