Sorry for the late reply...
FWIW, re: migrating Windows to new hardware, I've had it work, & occasionally not. I've got a running copy of Win11 24H2 that was originally Win7 Beta (!). RE: Windows builtin backup -- it works fine but the hassle is there's no bootable USB stick if you need one. The (semi) official workaround is to use the recovery environment if/when needed, I believe from an ISO if the RE on disk is gone.
In no particular order...
Backing up & transferring Windows...
It's more work, and some expense if you don't have spare drives handy -- the choice of course is yours.
You'll need a drive to store the backups & a USB housing for that drive or a drive dock. The drive should have enough capacity to hold both the backup of your current PC and the new one -- right click the drive in File Explorer, select properties, and then read the Used space. [Note: your backup will actually be smaller than that.] You'll also need disk/partition backup software. AOMEI has a free version of Backupper, and you can still find the free version of Macrium Reflect online [what I prefer, as long as it keeps working] at download sites like Major Geeks. Install the backup app on your Win10 PC, and use it to create the bootable USB stick. Then make sure that USB stick works on your new PC/laptop. Unfortunately there's no universal way of booting to a USB stick -- it varies by brand of PC/laptop, and sometimes also model, so you'll have to do some research, e.g., for HP I believe you hit the Escape key when the PC/laptop is 1st starting up from a power off state.
On your new PC/laptop make a copy of the C:\ Windows\ System32\ Driverstore\ FileRepository\ folder to the external drive or a USB stick. Shut it down, plug in the bootable USB stick and the external drive, boot to the USB stick, and back up the entire disk to that external drive. Then back up your Win10 PC to that same external drive, boot to the USB stick on your new PC/laptop, plug in the external drive, and restore the backup from your Win10 PC, replacing everything that was originally on its drive. When that's done, shut down, unplug the USB stick & external drive, and start the new PC/laptop. Win10 should start, though it may take a while looking for new drivers, and it may restart once or twice. Once it's running right click the Start Button, click Device Mgr. look for anything out of place, e.g., a device with no name, try auto updating that device, and if that doesn't work, have it search for a driver in that FileRepository folder you copied. Update the graphics driver, then download & mount a Win11 ISO from Microsoft, and run setup to upgrade to Win11 saving all your files & settings. If everything's OK afterward, go to Windows Tools and run Disk Cleanup to get rid of the old copy of Windows.
Note: *If* you're going to put your games on the external drive, create a folder for them on the external drive and move them before backing up.
Finding saved games files...
It's a hassle -- one of many reasons I don't like starting with a fresh copy of Windows. The folders where that info is stored aren't intended to be easy for users to find, and may be named the same as the game or it can use the publisher's name. You need to have File Explorer show hidden files and system files [set under Options in File Explorer]. Then look in C:\ ProgramData, C:\ Users\ [UserName]\ AppData\ Local\, and C:\ Users\ [UserName]\ AppData\ Roaming\. You can also check in Documents & C:\ Users\ Public\ Public Documents\.
Big Fish Game...
I'll try to find where the saved game data is on my wife's PC. I *think* the most likely problem is one or more of the files are corrupted, which can happen if Windows was writing to the hard disk/SSD when the power went out, or less frequently, if the drive screwed up when the power was cut. If scanning the drive in Windows -- right click the drive in File Explorer, select properties, then Tools, then the Check button under Error checking -- doesn't help, you'll probably have to reinstall the game, &/or the BigFish app. However I don't know if that will erase your saved game levels. If they're stored in one place you might be able to save that somewhere else, then copy/paste it into place after reinstalling.
New PCs/laptops...
The latest laptops tend to be Copilot+ PCs. They generally give better battery life than earlier models, but the extra Windows features may or may not be worth it to you. Copilot+ laptops [there are no desktop versions yet] have an NPU built into the CPU, which takes some of the load off the more power hungry GPU [graphics processor] for better battery life. However, Microsoft hypes the NPU as enabling AI on the device rather than in the cloud, adding features to Windows that are only available on Copilot+ PCs as part of their marketing. Some have new Qualcomm ARM CPUs, beefed up versions of what's in your cell phone, but while software support is growing, there are many thousands of apps & games that are not compatible. Windows for ARM CPUs can run most of that incompatible software [but not games] in emulation mode, but the results are very mixed. AMD & Intel, the traditional PC CPU makers, are trying to compete with Qualcomm's greater battery life, but for Intel at least, that means reduced performance compared to last year's models, which you may be able to find at reduced prices. That said, the latest laptop CPUs *may* have better graphics processing built into the CPU, depending on the CPU brand & model used.
Mini PCs generally use basically the same electronics as a laptop, without the battery, crammed into a small box often ~6 inches square. You use them just like a desktop PC, though they can be considerably cheaper, since you're saving the cost of a larger case, and power supply, which can amount to hundreds of dollars.
A regular desktop PC doesn't have the power constraints of a laptop or mini PC, so the CPUs are more powerful than the equivalent laptop models.
A big factor in laptop pricing is the display -- you can go from a basic display to an OLED that stretches almost edge to edge. An added GPU, or graphics card in a full-sized desktop PC, also adds a lot to the cost. Otherwise it's a matter of choosing the CPU, amount of RAM, and the size of the hard disk or SSD. You can find reviews with benchmarks comparing the performance of CPUs, which is straightforward for full-sized desktop PCs -- the mainstream CPUs are the i5 & equivalent under Intel's new naming scheme, and the AMD Ryzen 5600, 7600, & 9600 [the 5600 is the oldest, & the 9600 the newest]. Laptop CPUs are Much harder to compare because there are more models, the difference between one model & the next may be really minimal, and both the names & model numbers themselves can be confusing. Be careful because a laptop with an Intel i5 might for example come close to the same performance as an i5 in a full-sized desktop, or it may closer match the next step down, an i3. You really have to compare the full CPU model number. Almost any CPU will let you play casual games, but you'll notice the difference with a low powered CPU when you browse the web. My wife's laptop has an Intel i3, and it's usable. It handles her games -- Candy Crush and games from GOTD -- just fine, but you have to be a bit patient going online. Ideally you want an SSD rather than a conventional hard disk, especially with lower end CPUs, and 16GB RAM, though 8 or even 4GB will work -- with 16GB you don't have to worry so much having multiple tabs open in your web browser. 32GB is the becoming the new standard on Steam, and it's great to have, but if you see a great deal with only 16GB don't be afraid to grab it. If the internal SSD is too small to fit your games, they'll work on an external drive -- a conventional 2.5 inch hard disk or SSD in a $5-$10 external housing works fine -- that's what my wife's laptop uses. Note that you will have to create new shortcuts to the individual games.
Right now buying electronics is a little bit crazy. Tariffs have gone on & off, retailers have stockpiled what they thought would sell before tariffs took hold, consumers aren't buying, and a ton of people are out of work. You see higher than average prices with really good sales scattered here & there when retailers need to dump overstock. All you can do is be prepared, with a good idea of what you want and what you'll settle for, and watch for a deal that comes close enough. Note that Amazon's having another big sale in October, and so will everyone else to compete.