I'll just toss out a couple I've used in recent times. This one I got because it was one of the smallest I could find and has a few short cables built in, so easy to leave in a coat pocket indefinitely and be prepared if anything ran low. The built in cables are short enough I wouldn't count on them for charging WHILE playing, though. But the capacity is more than double Switch's, so all together it could more than triple your playing time.
This one is a bit larger and has no cables built in, but it doesn't cost much more and is double the capacity, so should be able to charge a Switch four times from empty if need be.
This is the one I have and it works great. I get about 5-6 hrs of solid play time from it:
https://www.amazon.ca/gp/product/B07YPY31FL/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1
I also bought this armband so I could strap the battery to my arm with a short USB cable:
https://www.amazon.ca/gp/product/B07JL74R2J/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
The battery doesn't have any clip or holder on it so the armband was the next logical option although I've seen quite a few 3D prinatable clips you can possibly use to mount it to the HMD directly.
I just converted my Vive Pro 2 to wireless using my OG wireless kit about a month ago. As mentioned you will need the VIVE Wireless Adapter- Pro Attachment Kit (amazon link) and you will need a battery. The OG battery will work until it starts getting under 60% and then the battery will not be able to support the wattage and repeatedly shut off the headset and turn it back on. Replacing the battery will fix this issue. This is the one that I purchased (amazon link) and it fits the KIWI strap perfectly (amazon link).
I would also highly suggest not using the original USB power cable that came with the OG battery. It is way too thin. Any thicker gauge USB 3 A male-to-male cable will do. I had an extra lying around my house that was the perfect length for my needs. Also, be sure to keep the wigig antenna high. As high as where most people mount their light houses. Any full obstruction between the antenna and the headset will cause drop outs (grey screens).
This all said, it cost me less than $100 to upgrade my old OG wireless kit to use on my Vive Pro 2. I rarely switch back simply because it just works so well. The resolution is about as good or better than my Valve Index wired. However, it has a lower framerate (90Hz max when wireless) and has artifacting at times due to the compression vs bandwidth of wireless. That being said - I prefer it for things like VRChat or anything that uses room scale. Sit down games, I use my Index instead. The FOV increase over my Quest 2 with AirLink as well as the comfort makes my Quest2 collect dust at this point.
Finally, the built in mic is terrible. I got a bluetooth mic to add on to the side (amazon link). Expensive, but I already had this for something else.
Just checked your link for the battery. That’s the culprit here. It’s not a QC 3.0 battery. I’d recommend returning the one you got and picking this one up:
INIU Portable Charger, 22.5W... https://www.amazon.com/dp/B07YPY31FL?ref=ppx_pop_mob_ap_share