Based on the max OS it looks like you must have a iPad mini (gen 1), iPad (gen 3), or iPad 2. All of those are 9-10 years old and got between 4-5 years of OS updates (unheard of at that time). Currently Apple is supporting iPads that are over 7 years old with the newest OS. You will not find a better option in the tablet space (or phone space for that matter).
It would be nice if Apple released one last security update for those iPads that included the newer root certificates so you could use the browser, or at least try since that version of Safari is old.
The bottom line is there isn't a company out there that supports hardware (of this class) that old. Linux or jailbreak are your best options if you want to keep using it for something but that hardware is pretty dated and I'd be surprised if you found a use (other than near-static display) that wasn't painful to use. Those early iPads weren't super powerful (as shown in how later iPads had a longer OS support window).
My iPad Mini 2 is just 1-2 years newer that what you have and I use it as a dedicated Paprika (recipe app) machine in my kitchen and it's so sluggish that I'll probably replace it in the next few years. Tech marches on and I find that most people that talk about wanting to use something like linux on an old device to be disingenuous, it's a painful experience to use hardware that old once you've used something newer. Even you seem to have not had a use for this for some years and now are angry that a piece of hardware you've not cared about for years doesn't do what you want?
> is Apple really doing their darndest to get me to buy a new iPad
The more I think about it, the only alternative would be linux. iOS developers have moved on and have no interest in supporting devices that old other than for maybe a hobby project. There isn't any money in it, it's painful to develop for, and the hardware is underpowered by today's standards.