Just after buying the Pencil, due to my use case detailed in point 2 of the side note in the question, I was getting the low battery message almost daily. Therefore, I searched the web for a way to get as close to a powered-off state in the Pencil as possible while it's not in use.

Removing Bluetooth pairing

Eventually I settled on going to Settings -> Bluetooth and unpairing the Pencil. When I needed to use it again, I just paired it again by taking out the cap and connecting its male Lightning connector to the female port in the iPad, then confirming the pairing when asked by the iPad.

I tested this and it seems to hold charge much better. I could go a day or two without using the Pencil, and when connecting it again, it had lost no charge at all, or at most a couple percent.

Need for periodic charge level checks

The main issue is that you have to remember to unpair it after use every single time. I realized my Pencil had died after a few weeks without using it, and it's not entirely impossible that I just forgot to unpair the Pencil at the time. The only solution I can think of, for now, to this issue is to add a reminder to check the Pencil's battery charge level every so often -- at least weekly, I'd say, and ideally daily if you don't find that too bothersome.

Charging tests

Also, I have performed charging tests with my replacement Apple Pencil, both sticking it directly into the iPad's Lightning port, as well as using the female-to-female Lightning adapter that comes in the Apple Pencil's box, which allows you to charge it from a regular USB-Lightning connector.

I performed two nearly full charges, from 5% back to 100%, using the female-to-female Lightning adapter connected to an authentic Apple USB-A to Lightning cable, connected to an authentic Apple wall charger (not sure if the 5 W or 12 W model though). Between the wall charger and the USB-A to Lightning cable I connected a USB ammeter. I verified the charging rate to be approximately 0.05 A (unfortunately I don't think this is a very accurate ammeter, so I wouldn't be surprised at all if the actual current deviated from this measured value by 10 or even 20 mA). Most importantly, the charging time in both cases was about 1 hour and 20 minutes, indicating a theoretical 0.75C charging rate, possibly closer to 0.8C due to inefficiencies. Either way, this is a charge rate that probably shouldn't degrade the battery and reduce its lifetime.

On the other hand, charging with the Pencil directly connected to the iPad's Lightning connector, also starting at 5% and ending at 100%, took only 20 minutes to charge. This indicates a minimum charging rate of 3C, probably more given that fast charge is even less efficient (I wouldn't be surprised if the actual rate is 4C). For energy-optimized cells such as LiCoO2, this is an extremely high rate that is sure to lead to battery degradation, as explained in the question.

Side note: there exist power-optimized cells with different chemistries such as LiMn2O4, and for these such high rates are not necessarily prejudicial. However, these batteries are heavier and larger than their LiCoO2 counterparts for the same capacity, so they're usually employed in specific applications such as power tools. Apple as expected doesn't disclose what chemistry they employ, but teardowns show that they go for LiCoO2 for most of their lineup, so it'd be slightly unusual for the Apple Pencil to deviate from this.

Recommended battery maintenance procedure

In closing, I would recommend the following procedure as an attempt to maximize the Apple Pencil's battery lifetime:

1. Unpairing the pencil in Settings -> Bluetooth after use;
2. Setting at the very least a weekly reminder (and if possible a daily reminder) to check the Pencil's battery level, just in case you forgot to unpair it;
3. When charging the Pencil, use the female-to-female Lightning adapter, connected to a Lightning cable, instead of charging directly from the iPad's Lightning connector. Use fast charging only when strictly necessary;
4. If possible, avoid keeping the battery's State of Charge permanently at 100% as it is somewhat harmful to the battery. 80% would be a huge improvement and 60% is ideal (no need to go below this.) -- a suggestion would be, after using the Pencil and when doing the weekly battery level check, connect it for a few minutes to the charger until the desired SoC is hit.

Yes, you can use the Apple Pencil 2 to collect information in a web page.

Yes, it can also be used to fill out <input> and <textarea> fields. However, it might not be in the manner that you imagine. If you're hoping that all browsers convert handwriting into computer text when you "draw" on top of an <input> - then you're unfortunately wrong. Instead you'll be able to use a virtual keyboard with the pen to enter text into <input> and <textarea> form fields.

Yes, you can use use Apple Pencil 2 to create files that can be "attached" (i.e. uploaded) from a web page. There's both built-in apps as well as third party apps that allows you to create PDFs, image files, etc. on iPads. These files could for example contain drawings made with the pencil. Browsers support the standard <input type="file"> field for uploads on the iPad.

If you want the user to be able to use handwriting directly on your web page without having to create PDFs or image files, then you can use the <canvas> element. You can easily find many tutorials on how to use the <canvas> element along with a few lines of Javascript to convert touch events from the Apple Pencil 2 into drawings on the canvas (either simple line segments or more advanced bezier curves). This is commonly used to support collecting signatures with the Apple Pencil 2.