Probably it will be a good idea to create installable script for using docker image

[twaik]

I wrote this one

#!/bin/bash
if [ "$#" -eq "0" ]; then
	set -- bash
fi

docker start termux-docker >/dev/null 2>&1 || \
	docker run --detach --init --name termux-docker -it termux/termux-docker:latest
docker exec -itu system termux-docker "$@"

Using this I can invoke termux commands from my regular shell like this.

termux apt-file search xcb-image.pc

Or simply enter termux environment with termux command.

[robertkirkman]

This scenario is very generic, not just to Docker in general, but to containers in general as a whole, one of the most common examples of which is Distrobox, which is a wrapper around Docker and/or Podman that sort of already implements that concept generically in a container-agnostic way.
https://github.com/89luca89/distrobox/blob/main/docs/usage/distrobox-enter.md#examples

distrobox-enter my-container -- echo 'example'

Does that make this a little bit out of scope, since it seems like the "generic solution" would simply be for the user to import the container to a Distrobox configuration and then use the Distrobox wrapper features to do almost exactly the same thing you described?