If you've got a full system backup, or even just a backup of your EFI System Partition (ESP;
/dev/sda1 in your case), you should be able to restore the ESP and everything should be fine. (You'll need to edit
/etc/fstab to refer to the ESP's new serial number ["UUID," which it really isn't.])
Failing that, it's best to restore Windows to bootability first. This is because Windows tends not to play nice with other OSes, so if you restore Ubuntu first and then restore Windows, the computer will end up booting straight to Windows. This problem is not difficult to fix if you know how, but it's easier to restore Windows first and then deal with Ubuntu. As to how to restore Windows to bootability, you should ask about that on a Windows forum. You'll need a Windows emergency recovery disk for your Windows version, though. You can probably find one of these online, or create one from another computer that runs the same version of Windows.
As to restoring Ubuntu to bootability, there are several ways to do this. The two easiest are:
- Boot Repair -- The Boot Repair tool can install a fresh copy of GRUB on the ESP. The trouble you encountered with it most likely means that you booted in BIOS/CSM/legacy mode rather than in EFI/UEFI mode; or maybe if you tried running it when
/dev/sda1 used ext4fs, that could have thrown it off. Controlling the boot mode (BIOS vs. EFI) of a removable disk can be tricky if you don't know what you're doing. The best way to do what you want is to go into your firmware settings and disable the CSM (aka "legacy boot support" or "BIOS boot support"), but details of how to do this vary greatly. If you boot the external medium by using a boot menu, it may have two options to boot your medium, one of which includes the string "UEFI" and the other of which does not. Pick the option that includes "UEFI" to boot in EFI mode. See my page on the CSM for more on this topic.
- rEFInd -- You can download a USB flash drive or CD-R version of my rEFInd boot manager and prepare a boot medium from it. When you boot from that medium, it should give you options to boot both your Linux distributions. (If you do this after you get Windows booting, rEFInd should also show you a Windows boot option.) If you boot into Ubuntu, you can then install the rEFInd Debian package or PPA; or you can simply use this as a way to boot into EFI mode and then run Boot Repair. If you install rEFInd to your hard disk, it will take over as your primary boot manager, bypassing GRUB.
I've never before heard of BunsenLabs Linux. In theory, either of the above methods should pick it up and present it as a boot option; however, it's possible that this won't work correctly. If you have problems, you could try the other recovery method or work to fix the problem in whichever boot manager you decide to use.
Moving forward, you may want to back up your ESP to make for easier recovery from such problems in the future. Ubuntu normally mounts the ESP at
/boot/efi, although you'll need to edit
/etc/fstab to get your modified ESP to mount there by default. (When you created a fresh filesystem, that changed its serial number, which is called a "UUID" in
/etc/fstab. Your current ESP has a serial number of 71B1-C511, according to your Boot Repair output.) A file-level backup, using
cp, or other tools, should work fine. Copy everything to a USB flash drive and you'll be able to restore it all pretty easily should you run into a similar problem in the future.