Thank you for your birthday well wishes! It wasn't a good birthday though, it's always hard for me due to grieving.

I was looking for a higher mAh buck converter for faster charging and found this one on Amazon. Will this suffice? Will of charge faster than the module you linked me to and is this at least equivalent to it in terms of overcharge/overcurrent protection?

As for the external charging solution, it's simplicity is great but I want a project, that's why I'm not simply resorting to rechargable AAs. Now I will say that, I am very intrigued by the charger you showed me, that's something I would keep on hand to ’correct‘ or level them out batteries and test their life etc since I will be using the built in AA battery holders and won't be spot welding them together with the nickel strips.

I want to revisit my idea of an external charger. When I misinterpreted what an external charger would consist of? Would I be able to build something like this: mains 5v 1a USB charger connected to the input side of Li-ion charging board>female USB Type-A plug on the output side of Li-ion charging board>USB Type-A to Type-C cable>USB Type-C module on controller>module connected to +/- side of batteries>batteries connected to buck converter input>controller connected to buck converter output.

Would that work for me? Is it safe? In my mind, since the batteries are technically connected to the charging board when a USB cable is connected, it would still have that protection, it would just be external rather than inside the controller. I'm a noob though and don't know all the benefits and drawbacks of a lot of things, even though I've been tinkering my entire life, I'm just now getting to the point of wanting to do cool stuff.

The numbering convention for LiFePO4 is the same as far as I know.

The easiest thing to do is just buy a charging circuit. The standard TP4056 chargers you linked will not work here though -- their cutoff voltage is too high and will damage the LiFePO4 cells. Lithium-polymer cells have a cutoff voltage a bit north of 4v, LiFePO4 is around 3.6V if I remember correctly.

You might try finding a module based on CN3058E, TP5000, or MCP73123. This looks like an ok example of the former, but maybe hard because you need to build it yourself, and the components are a bit small for a beginner project: https://oshwlab.com/wagiminator/cn3058-lifepo4-power-board-ls-3v3

Here is a module you can 'just buy' based on the TP5000, you just need to break a trace to set it to LiFePO4 mode: https://www.amazon.com/TP5000-Lithium-Battery-Charging-Charger/dp/B07VKJ6XPZ

And here is an in-depth review and characterization of that board: https://lygte-info.dk/review/Review%20Charger%20TP5000%204.2-3.6V%20module%20UK.html

Overall the charger options are not quite as good as I thought they would be by now! But this one above looks OK.

If it proves too annoying to find small charger modules, just buy an external charger (these are easier to find and plug directly into a wall outlet) -- this lets you decrease the component count that goes in to your devices, making that part smaller, and maybe reducing cost per device.

For DC-DC conversion, I made a mistake -- you probably need a buck-boost circuit. This raises the voltage to some high amount, then drops it down to an amount you specify. The reason for this is that LiFePO4 is around 3-3.6V so a bit too close to the 3V systems you might frequently want to connect it to. This configuration will allow for a wide range of voltages to be produced, and it's relatively efficient. Better than 85% usually. There are many modules that work fine -- I like this one: https://hshop.vn/products/mach-on-ap-dc-dc-buck-boost-conveter-b6289u-5-3-3vdc-0-6a

You can probably find that online and available to you. The reason I like it is because it has an 'enable' pin. When you want the device to always be enabled, you just connect that to the + output of your TP5000 circuit ( or the battery + if not using it). When you want a power switch, just connect it between the battery/TP5000 + output and that pin (and leave the output of the voltage converter just... always connected to whatever you are trying to power). The reason to do this is because these DC-DC converters have what's called quiescent current draw, where they draw power even when no load is connected (usually tens of millamps, which I always found surprisingly high). When the enable pin is logic LOW (not connected to a positive voltage like battery +), it properly shuts down the DC-DC converter and consumes very very little power. Then as soon as you apply a small signal to that pin, it happily starts up.

Anyway as you can see, battery powered systems are quite an engineering rabbit hole! Currently I am designing a system that needs to run for a minimum of 3 years off a single coin cell (CR2032) -- much longer is theoretically possible too, 70 years even -- if you're lucky enough to get a coin cell that has a shelf life that long! Modern low power systems are really cool!

EDIT: the cells in steel casings normally include a small chip that prevents overdischarge (I tend not to trust it though, but I'm just paranoid). The TP5000 charge management chip on the charger board also offers overdischarge protection, both in terms of voltage dropping too low and taking too much current at once. It also contains some thermal monitoring, and overcharge protection (as long as you break the solder connection as instructed). To work this out, I read the datasheet translated from Chinese:

https://pdf.voron.ua/files/pdf/Microshema/TP5000_auto_translated_.pdf

EDIT2: You should go buy a cheap multimeter, to make sure everything is working as you expect (e.g. output voltage) before connecting it to something expensive. You can get them at discount/dollar stores for like 5$ I think.