It was recommended by the the IT department that our installation run in a Docker, instead of installed as it currently runs.
Congratulations for your IT department. 
What it entails?
Better maintenance, better isolation, much better performance (than VM), easier upgrade, easier portability, easier scalability, efficiency, consistency, flexibility, continuous Integration, rapid Deployment, reusability, modularity…
Any downside? IT services need to learn how to work with them.
I made this presentation in 2019 (half translated to English last year) to explain the benefits of docker:
https://hackmd.io/@marcbria/docker4dummies2024
My current installation is over 17 years old (currently on 3.3.x and upgrading to 3.5) has custom plugins and almost 10 journals.
I have 50 journals with single-tenant and journals with almost 20 years.
I assisted multi-tenant services with 20-30 journals to move to containers and all works great.
How stable and/or recommended is it to move to Docker?
It’s very stable and from my experience, I full recommend it.
My life as a sysadmin is much better now. 
Why is not yet more extended in PKP? Probably @asmecher (as a PKP tech lead) could give you more clues, but in my opinion, containers are not yet the official recommended way to work because in our community we have a lot of installations that are still in traditional LAMP hostings… well, and also because in PKP team (I’m not in PKP’s staff) we still don’t have yet any expert to hold the image creations and documentation (I’m doing the job as a volunteer) but things are changing…
What benefits will I have? What downsides?
See above.
Adenda
This repository is holding an explanation about how to easily install ojs with docker. Documentation is also included there.
We are building new images here (that will replace former repository soon).
This week we made relevant changes in our “official” docker images (between quotes, because as said, those images are a community effort and not yet maintained by PKP). More information published here.
Better official documentation about docker (ie: a “howto upgrade” expansion) it’s on its way.
I’m working on this project (called “dojo”) to easily hold a full service (with docker and ansible), but it’s not yet ready for production if you don’t know what you are doing.
If you got any trouble, or you have new doubts, please open a new thread and mention me.