First of all, welcome to CFC!
I'm not the right person to answer the question definitively, but I'll tag
@AlanH , who is our resident self-proclaimed Mac addict. I don't know whether he has switched to M1 yet, but he's probably better-informed if there is a chance of running Civ3 on M1.
That said, of what I know, there are two main hurdles. The first and perhaps biggest is that Catalina (10.15) dropped support for 32-bit applications, which includes Civ3. So even if you were on an Intel Mac, with 10.15, I don't think you'd be able to run it.
The other is that Civ3 is compiled for Intel processors (or for older copies, PowerPC processors). It
might be possible to run Civ3 with Rosetta, if that were the only hurdle. But I don't think Rosetta on M1 would support 32-bit Intel applications, since 10.15 dropped support for them.
The other alternative for Civ3 compatibility on Intel Macs running 10.15, to run Windows on a virtual machine, is to the best of my knowledge not possible on M1 Macs.
So that leaves one last-ditch option that would work for some other games, but not Civ3: NVIDIA's GeForce Now, which
recently added M1 compatibility. The way it works is you download a program that connects you to a remote machine with a powerful graphics card, and can log into your Steam library from there, and stream Steam games remotely. Unfortunately, 2K (Firaxis's parent company)
removed their games from GeForce now, so I don't think that would work either.
Hopefully AlanH has another more promising idea, but...

It might be a good idea to keep another machine around to satisfy your Civ3 cravings.