This is a BIOS vs. UEFI thing, it has nothing to do with Windows or Secure Boot or the TPM requirement.
When you do an initial OS install today, you have to boot the computer in the mode that you intend to use (Legacy BIOS / CSM mode vs. UEFI mode, with or without secure boot). This is the case with Linux too. You can't really just switch modes afterwards.
For Windows, you'll definitely need a reinstall. (Edit: I didn't read your post carefully, apparently there's a tool to fix it? Neat!)
For Linux, there's probably a way to re-bootstrap everything yourself (reorganize your partitions, create the EFI partition, copy your kernel and initrd, etc.), but reinstalling is preferred, and will almost certainly be easier.
Several years ago I screwed up a Windows/Linux dual boot by installing one under BIOS and the other under UEFI. The only way to select the operating system was to go into the firmware settings and flip the CSM/UEFI bit each time. That was an annoying week, but the fix was to turn off CSM and reinstall everything under UEFI.
There is this base assumption that UEFI=GPT and that BIOS=MBR which is only partially true (at least for windows 7/8/8.1/10).
In fact the UEFI is perfectly capable of booting from both GPT and MBR disks, the issue is only that when you install an OS in CSM (or BIOS) on a MBR disk, the OS loader/boot manager installed will be the one needed for BIOS booting, and the UEFI one won't be installed.
Besides there is the requisite of having a FAT32 (this can usually be worked around with a UEFI NTFS driver).
But a "normal" BIOS install on MBR (with a dedicated, without drive letter automatically assigned, FAT32 primary partition dedicated to the boot files) can be booted just fine in UEFI by simply adding to that partition the needed UEFI loaders.
The opposite (booting with BIOS from a GPT disk) is as well possible but needs some non-standard modifications/hacks to the disk MBR, that - although proved in the years to be "safe" remain a sort of hack (not recommended if not really-really needed).
>When you do an initial OS install today, you have to boot the computer in the mode that you intend to use (Legacy BIOS / CSM mode vs. UEFI mode
That's one worthwhile technique.
Not many users want to go much further since then you need at least twice as many boot files as the minimum and it's best to test each configuration thoroughly.
If you're dual-booting you are already putting twice as much effort into OS installation & maintenance already, this is not really popular but I did post my latest findings just a couple days ago how I use 4 sets of boot files for W10 & Ubuntu on BIOS & UEFI:
I don't think you need to reinstall much. As long as you have a UEFI-compatible bootloader after converting your hard drive to GPT partition scheme, your UEFI should pick it up. Windows certainly installs one.
When you do an initial OS install today, you have to boot the computer in the mode that you intend to use (Legacy BIOS / CSM mode vs. UEFI mode, with or without secure boot). This is the case with Linux too. You can't really just switch modes afterwards.
For Windows, you'll definitely need a reinstall. (Edit: I didn't read your post carefully, apparently there's a tool to fix it? Neat!)
For Linux, there's probably a way to re-bootstrap everything yourself (reorganize your partitions, create the EFI partition, copy your kernel and initrd, etc.), but reinstalling is preferred, and will almost certainly be easier.
Several years ago I screwed up a Windows/Linux dual boot by installing one under BIOS and the other under UEFI. The only way to select the operating system was to go into the firmware settings and flip the CSM/UEFI bit each time. That was an annoying week, but the fix was to turn off CSM and reinstall everything under UEFI.