So, since it seems you are running an old style mechanical hard drive for both the operating system AND the flight sim files, then I'd have to say that perhaps that might be your best low cost option for an upgrade or upgrades, and has the added benefit that if you should happen to upgrade the whole system anytime in the next year or two then any SSD you puchase can be used with that system as well, meaning it is not a waste to spend money on one whether you have plans to upgrade or not.
I would really recommend upgrading BOTH drives, so that you have two SSDs, one for Windows and applications and one for your game files. You can then ALSO use those mechanical hard drives for backup images of Windows, any important personal files and your game files, so that you always have backups of everything important which you absolutely SHOULD have no matter what. Always have AT LEAST two copies of anything important because it's never a question of IF a drive will die, it is only ever a question of WHEN. And real life isn't like the movies. When a drive dies, even if you could afford to send it to a data recovery specialist, it is not particularly common that they are able to rescue all or in some cases even ANY of your data. The best recovery method is to always have a backup. That's actual insurance rather than a pipe dream or wishful thinking.
I think that you would be likely to see a real improvement and a system that "feels" much "snappier" if you upgraded both drives. While you won't see actual gaming performance improve due to the addition of an SSD you WILL see Windows and therefore some aspects of the game performance improve because Windows is constantly calling on data from the drive for various processes including for your game engine, so in that way as well as in general usage, you'll feel the difference markedly improved.
You could do something like this and then either do a clean install of Windows to the new SSD or clone your existing Windows installation to it. As well, you can simply move your game files from their current home to the other new SSD if you chose to do this.
Since your motherboard supports PCIe NVME M.2 drives, I'd probably recommend doing something like this for the OS drive. Keep in mind, there ARE lower priced models that are still relatively good products, but they are primarily going to be ones without any DRAM cache, and will therefore tend to be considerably slower than models with cache and a good controller like this drive has. For the price, very difficult to beat.
PCPartPicker Part List
Storage: Western Digital Black SN770 1 TB M.2-2280 PCIe 4.0 X4 NVME Solid State Drive ($45.90 @ Newegg)
Total: $45.90
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2023-06-11 13:55 EDT-0400
And then for the game files, something like this would be perfectly suitable and would certainly benefit you in terms of not having to wait while around for days while things load whether it be levels, new maps and terrain, textures or other game data. Not to mention, it frees up your HDDs for backup duties like I said before. Plus, given the idea that those HDDs are likely several years old at least, it puts your operating system and flight sim files on newer hardware that is less likely to die on you anytime soon.
Again, there are less expensive 1TB SSDs out there, but this is the least expensive model that has both a DRAM cache, which matters, because it makes the drive much more consistently faster, and a five year warranty compared to only a 3 year warranty for pretty much every non-DRAM budget model that is less expensive. Certainly those DRAM-less budget models are still an option if the budget is REALLY very critical, and will still have much better performance than any hard disk drive, but the ten bucks or so that you save are generally not worth the savings when you compare the performance, reliability and warranty of them with a drive like this.
PCPartPicker Part List
Storage: Crucial MX500 1 TB 2.5" Solid State Drive ($51.99 @ Amazon)
Total: $51.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2023-06-11 14:07 EDT-0400
So, as far as not getting immediately out of hand with the cost of hardware or an upgrade, I think those two options are your best ones for a relatively budget friendly upgrade that doesn't totally break the bank or require a serious investment to obtain.