Docker network pools are huge by default. I had to change this as well.

This article covers the issue and the solution in detail:
https://straz.to/2021-09-08-docker-address-pools/

If you just want the solution, skip to the section titled How to configure docker to allow >500 bridge networks. I think you'll need to remake all your networks after making the change, if I remember correctly.

Here's my config now:

$ sudo cat /etc/docker/daemon.json
{
  "default-address-pools": [
    { "base":"172.16.0.0/12", "size":24 },
    { "base":"172.17.0.0/12", "size":24 },
    { "base":"172.18.0.0/12", "size":24 },
    { "base":"172.19.0.0/12", "size":24 },
    { "base":"172.20.0.0/12", "size":24 },
    { "base":"172.21.0.0/12", "size":24 },
    { "base":"172.22.0.0/12", "size":24 },
    { "base":"172.23.0.0/12", "size":24 },
    { "base":"172.24.0.0/12", "size":24 },
    { "base":"172.25.0.0/12", "size":24 },
    { "base":"172.26.0.0/12", "size":24 },
    { "base":"172.27.0.0/12", "size":24 },
    { "base":"172.28.0.0/12", "size":24 },
    { "base":"172.29.0.0/12", "size":24 },
    { "base":"172.30.0.0/12", "size":24 },
    { "base":"172.31.0.0/12", "size":24 }
  ],
  "log-opts": {
    "max-size": "1g"
  }
}

It sounds like your outgrowing docker. Maybe switch to Kubernetes at some point?

Only if there was IPv6: https://docs.docker.com/config/daemon/ipv6/

Just run all your containers with IPv6 randomly generated prefixes and this won't ever be a problem, you'll also get more IP spacing than you'll ever require. Then use your reverse proxy to convert between the "public" IPv4 space and the internal docker IPv6 networks.

Another option is to reduce the size of your IPv4 pools like this guy described.

then you'd limit the existing network addresses using subnets, as suggested by another answer in that question

sounds like your issue isnt with the number of networks, but how youre addressing them. fix that.

if youve got a container that only needs a single or a few ip's then its defined network should reflect that.