Linux installer cannot see my NVMe drive at all, so there is no "install alongside Windows" option

Quick way to confirm the diagnosis before you touch any settings, from the live environment you already have booted: open a terminal and list the block devices, then list the NVMe devices specifically.

If the disk is absent from both, it is invisible at the kernel level and it is a controller or firmware problem: the installer is innocent. If the kernel can see it and only the installer cannot, that is a completely different and much rarer situation involving the partition table.

Thirty seconds, and it tells you whether the sequence above is worth doing.

Second the storage mode as the overwhelming favourite. Two smaller causes worth knowing, since they produce a similar-looking dead end:

Secure Boot with an installer that is not signed for it. Usually this stops the live environment from booting at all rather than hiding disks, so it does not fit your description - but if you disabled it to get this far, remember you did, because it affects what you do afterwards.

A pre-existing four-primary-partition situation on an older MBR disk. Not your case on a recent NVMe laptop, but if someone lands here with a disk full of vendor recovery partitions and no free partition slot, the installer will refuse to offer alongside-install even though it can see everything.

Also: check in the firmware whether there is a separate setting for the specific NVMe slot. On some machines the mode is per-port and changing the global one does not cover the slot the drive is actually in.

This is almost always the storage controller mode, and it is the single most common wall people hit installing Linux on a laptop that shipped with Windows.

Many laptops ship with the NVMe controller in a vendor acceleration or RAID mode rather than standard AHCI/NVMe. Windows works because the vendor driver was loaded at the factory. Linux has no such driver, so from the installer's point of view there is no disk at all - which matches your symptom exactly, including the empty manual partitioning screen.

The fix is to switch the controller to AHCI, but you cannot just flip it, because Windows will then fail to boot for the mirror-image reason: it will be looking for a driver it no longer needs and will not find the disk. Doing it in the wrong order is how people end up reinstalling Windows.

The safe sequence, which works reliably:

1. In Windows, tell it to start in safe mode on the next boot. There is a supported way to do this from the boot configuration; you are telling Windows to load a minimal driver set next time.
2. Reboot into firmware, change the storage mode from the RAID/acceleration option to AHCI.
3. Let Windows boot into safe mode. It detects the changed controller and installs the standard driver.
4. Turn off the safe-mode flag and reboot normally. Windows now boots fine on AHCI.
5. Boot the Linux installer. The disk is there, and the install-alongside option appears with it.

Two other things to clear before you start, both of which can block you independently:

BitLocker. If Windows drive encryption is on, suspend it: or better, decrypt - before repartitioning or changing firmware settings. Changing storage mode alters the platform measurements the encryption keys are sealed to, and you will be asked for a recovery key you may not have written down. Get the recovery key out of your account and save it somewhere physical regardless.

Fast Startup. Turn it off in the Windows power settings. With it on, "shut down" is a hibernate, the Windows partition is left in a dirty state, and any installer that touches it can leave you with a damaged filesystem.

Do those two first, then the storage mode dance, then install.

One more for the pre-flight list: make sure the unallocated space you created is on the same disk you want to install to, and that Windows did not leave a recovery partition sitting between the shrunk partition and your free space.

It does not stop the install, but it constrains what the automatic option will offer you and occasionally makes it decline to offer anything at all. Easier to look at the layout now than to work out why the installer is being unhelpful later.