Went through this exact same headache after updating my a7IV. The firmware is super picky now and keeps flagging my older third-party cells. If the budget is tight for your NYC shoot, there are a couple options that actually work without that annoying popup every time you turn the camera on. Here is what is working for me right now:

• SmallRig NP-FZ100 USB-C Rechargeable Camera Battery - these are great cause you can charge them directly, and they dont trigger the warning on the latest firmware.
• Neewer NP-FZ100 Replacement Battery and Dual USB Charger - the batteries are decent backups, and the charger is solid for the price.
• Sony NP-FZ100 Rechargeable Lithium-Ion Battery - obviously the safest bet if you can swing at least one more. The SmallRig ones are the best middle ground. They feel sturdy and the capacity is close to the original. Just get the newer version with the USB-C port on the battery itself... usually avoids the chip issues.

In my experience, the firmware issues stem from outdated decoding chips. I've tried many over the years and found these reliable for the a7IV:

• SmallRig NP-FZ100 USB-C Rechargeable Battery
• Nitecore USN4 Pro Dual Slot USB QC Charger The SmallRig cells are solid because they allow direct USB-C charging. It is basically a fail-safe if your charger goes down. Just make sure they're labeled as fully decoded so you dont get that warning during the shoot.

I am dealing with the exact same issue right now and it has been a total headache. 1. I have been seeing those same compatibility warnings for about a month now since I updated my a7IV.

• It is honestly pretty stressful because I really value reliability and I am terrified my camera will just die mid-shoot.
• I still have not found a solid answer or a brand I can truly trust yet... it is just so frustrating. I am definitely keeping a close eye on this thread for any real solutions because I'm in the same boat.

Bump - same question here