Another option is to try to find an old and super cheap laptop and use that instead. Maybe find one with a broken screen or busted keyboard or something that you won't care about.
This is essentially what my MBP with butterfly keyboard has been relegated to in life. The keyboard is unusable, it's too expensive to repair, but it's not a shitty enough computer to just throw away, and there's practically no trade-in value either. So, there it sits in a closet, on a top shelf, just acting as a remote device doing random things as I assign it tasks.
However, cheap is not how I would have described it ;-)
If your laptop's USB ports will provide enough amps, that could work.
Doesn't the Pi 3 expect up to 2.5 amps? I imagine some of that is for powering USB ports, so you could probably get away with 1.5 amps if you're not using them, but even that's a lot for laptop USB. I'd be surprised if any offered more than 1 amp.
Are there any you could recommend? Most that I have looked at cost about the same or more as a Pi in the first place and don't even come with batteries.
I use a big one (think CyberPower and APC) for a small collection of devices including some network hardware. Smaller ones from those brands or AmazonBasics cost around 50 bucks, battery included. I tried a UPS hat, which would have been the most clean-cut solution, but it failed and the battery bloated.
If you power your Pi via USB just use a phone USB bank that works via passthrough. (I don't actually have one to recommend but just one that can charge and discharge at the same time).
> one that can charge and discharge at the same time
I did some research into this as well and I'd gladly consider this as an option but most power banks can't do this. And the ones that do don't tend to advertise it. Every time someone says they found one that can do this, in some forum or whatever, they are no longer available to buy.