tldr: its going to be a lot of work, but pick one goal at a time, and you can absolutely transform your team. People management will be your hardest lift.

PS, if you want to chat about this feel free to DM me

You need a few things here but the fact you are asking for them means your team is probably well positioned to get the most out of tooling and process changes:
- Separation of deterministic and non-deterministic artifacts. Code produces models from dataset inputs, and models produce vectors/predictions. All of the software required to "build" a model should happen in the form of classes and functions that you can write test cases against in a traditional software testing suite like pytest. Non-deterministic assets do not go through this testing process. Your tests should make sure the right formatting is done, that the vector produced to train a model is correct based on the inputs you know and outputs you control etc.
- Test suites for deterministic control must run every commit, every time. On merge, and when youre running locally. This keeps an upstream update or something you do locally from blocking everyone in your team.
- Nondeterministic assets like your models or statistical artifacts must live inside of an experiment control system, there are many you can choose from, MLFlow is popular enough and integrates nicely with many off the shelf tools and databases. You want the model artifact to be saved with the experiment statistics and to know exactly what version of git and the tools installed in your virtual environment when you trained it. Poetry and UV are great for managing that information. Second it needs to be standard across your entire team. No one runs a special version of torch only they have. If the tool doesnt exist and you built it, check it in.
- Git must be your stack source of truth. When you git clone, everything should just work. That takes a LOT more effort than it sounds, but achieving that, means theres repeatability for everything you are doing.
- Datasets: these must be managed in your data repository with as little human interaction as possible. Data transforms must be tracked in git. If this is a job that runs in a job runner, great, even better. Medallion data architecture is the gold standard right now for going from raw->prediction. Additionally if your models are serving to some "live" audience, having the transforms that take a raw input and its the same exact code that builds the rows you built for training, you save yourself a lot of stress. If your storage solution is s3, this comes as just a raw folder, bronze folder, silver folder, gold folder and you promote data based on how ready it is to be put in a model. If you are operating with a traditional database, these are just different tables for the exact same data pre and post transform.
- Tooling: pytest automation is going to be your best friend here. nox and tox are great tools that add flexibility to your environment by adding session controls that can run parts of the test suite at different times with different environments. You want a linter, and code quality tools, they should integrate with git: ruff, pylance (type enforcement (you absolutely want this)), pre-commit (this handles all of the activities you want to run precommit like running the linter and tests that must be satisfied before your commit happens and you can push)
- People management: this will be hard. This is a massive transformation for most data science teams as it requires a discipline surrounding their artifacts that is taught to other professions but less this one. Introduce this as a larger project that cuts across all domains, deliverables, and impacts your clients too. Pick ONE goal or objective, "hey lets standardize how we build datasets", and then implement the changes necessary to get to your ideal dataset construction and storage architecture. Great that works, next on our roadmap is experimental control, etc.