It depends on what kind of devices you’re using.
It’s my understanding that SIM cards in phones are just to tie an account and identity to your phone, for purposes of enforcing people to be paying customers for the phone/data services, and tracking your usage based on what level service you’re paying for and what you should receive (5GB of data monthly, unlimited texts, etc)
But if your phone doesn’t have a SIM card in it, its still connecting to cell towers for purposes of emergency dialing, and the phone itself can continue to be tracked by cell carriers based on what physical cell towers its connecting to, as you travel around. The cell phone modem itself can control and connect to networks independently of what the OS running on the phone tell it to do, its a self contained black box.
If you have something like a desktop or laptop, both Intel and AMD have “management engines” embedded in the CPU’s themselves that can take control of the device for purposes of shutting down, wiping, etc a company machine that has sensitive information or access on it, and has been reported stolen, not returned by an ex employee, etc. These management engines have direct access to the network stack and can phone home whenever a network connections is present, either from a WiFi network, physical Ethernet cable, or 4G/5G WWAN card.
https://en.wikipedia.org/wiki/Intel_Management_Engine
If you have a device that is basically air gapped, no WiFi, no cellphone chip, no bluetooth, etc, than it’s still possible to exfiltrate information off the device, but the software running on the device would have to be programming to be searching for methods to do that. Your average device, unless it’s running malicious software, probably won’t be doing that.
I usually check ebay when i need electronics batteries, but you have a chance of a seller selling knock off batteries that as you said, could be sketchy. I’ve personally never had an issue, but YMMV.
https://www.ebay.com/sch/i.html?_nkw=ups+battery