If everything goes well, it looks like I'll have a laptop with specs like these:
CPU: Intel Celeron
RAM: 4GB
Boot drive: 500GB SATA SSD
Other drive 64GB eMMC (soldered on, so can't remove this one)

Now, I know that there's a lot of discussion about the case of a computer having two storage devices, one fast with low capacity and one slow with high capacity (my desktop is like this, actually), but there really isn't much discussion for the case when one storage device is *clearly* better than the other (one drive is faster and higher capacity than the other). So, here's the question:

What should I put on the eMMC drive, which is clearly worse than the SSD that I'm planning to put in this computer?

Long term back up files.

so, are we going to guess what kind of files you have? Music perhaps, or phots, or ducuments, or films, or.... whatever else you might want to store?

There's some virtual machine images on there currently, as well as a few games and, of course, the OS.

Thing is, my plan is to install the OS on the other drive so it boots faster, but the other drive also has room for everything else.

There was some music, but I moved it over to a 32GB SD card, which has the advantage of being removable (unlike the eMMC).

I'd use it as a backup for critical files that you have stored elsewhere - so if there's anything on your SSD that you don't want to lose, stick it on the eMMC as well. Not an ideal backup as it's still in your laptop, but if your SSD dies then you've got an additional backup to your external one.

My recommendation: nothing. eMMC is just USB-stick/card level flash memory with a faster controller - it has neither stellar performance nor stellar endurance. I'd just blank it and leave it there unused. 64GB is not a lot these days anyway.

you are kind of answering your own question here, so i am not sure what to say apart from the very obvious that you most likely already know.

Yes, use your fastest drive for the OS.

If you have any software / games that loads a lot or uses the HD a lot put them on the fatstest drive. Old games or small, which do not laod much and is not very drive intensive, you can use on the slower drive.

If you use for example Photoshop a lot - put it on the fastest drive, but you can use the slower to save work files or the final outputs. (swap photoshop with any other software)

Use the slower drive for files you just want to store (i.e. images or documents). Also use to slower drive to store any back-ups.

what else?

it works for all cases where you want to use two drives - one slow and one fast. The size of the drives is really not of any relevance (unless your fast drive is too small to hold for example the OS). The only other option is to ignore the slow one.

Once you get your primary system drive configured how you want, take an image snapshot and store it on the smaller drive. Make a second external copy too, of course. But you'll have a built-in backup that you can easily roll back to.

Or just leave it as blank overflow storage. If you ever get close to filling up your primary drive then you've got 64GB of extra space to dump lesser used data to while you save up for a bigger primary drive.

Ok, but if everything goes spectacularly awry, what kind of laptop will you have then? Since you will be running Linux on it...

...I think maybe /boot. That is what I did with Raspberry Pi4, keeping /boot on the MicroSD card and rest of the filesystem on an external USB HDD. Then again I guess the eMMC is slow (also for /boot), but then if you want to use it for something...

Alternatively, if you use some "backup" option like Timeshift or such, maybe those could go there? Would they fit into 64GB? I guess? (To Windows users, they are somewhat like "restore points" on Windows, I guess...).

ROMs / emulators, music, images, docs, textbooks, videos, low priority software, etc.

use it to make music like star wars intro
maybe you need more thou

That's not going to work, as the eMMC is solid state storage that doesn't make any sound.

so it is even less useful
soldered hmm ? so you cant even put it into the microw to make it pop , not cool
just forget it then