How to find collaborators for just writing and formatting manuscripts

Writing the manuscript is a significant scientific contribution. Is your research so trivial that anybody can interpret the data that you give them and write to a high scientific caliber on them, with no further inputs from you? Most likely, you'd need to also provide them with a rigorous analysis of that data, probably in writing form, since they might no share an office with you, and also for record keeping. That explanation becomes the crux of a paper that you could write yourself in the first place. The time spent explaining the data to someone not involved in an experiment will be greater than just writing the thing yourself. You'd be only saving time on tiny matters of sentence formulation, if you'd even save time at all.

Formatting a paper in my experience doesn't take that much time, so I'm not sure where you're coming from in on that point. Most journals provide you with a template that you can literally copy paste into. If something is straightforward as you say, it shouldn't take that much time at all. If by "getting bibliography", you mean compiling the bibliography, that will also be something that only you, being familiar with the experiment, can provide. A bibliography should be something that arises naturally from the need to reference previous methods/works for your analysis, not a chunk that you copy paste between papers without thoughts.

If you mean that they also do the data analysis, then they just become a regular scientific collaborator, with full authorship rights.

Not enough time to write papers

Producing papers is a core part of your job. You cannot avoid this. Delegating writing (to non co-authors) is surely plagiarism. Nonetheless, you might be able to improve your efficiency.

Writing introduction and methods sections. Presumably, you made some notes when you started work, e.g., you formulated some hypothesis. Instead of writing such notes, you could write the first draft of the introduction.

Bibliography. I'm not sure what "getting [a] bibliography" means. Do you mean writing a "literature review"? If so, then that's something that also comes from your initial notes, when you establish the context of your proposed research in relation to the existing literature.

Co-authors. You can distribute the burden of writing amongst the group. In particular, PhD students can do the vast majority of any writing when they are a co-author.

Formatting manuscripts

This task typically isn't time consuming. Nonetheless, you could always hire an undergraduate to the work. You could hire me too -- but I doubt you could afford me!

The assumptions that you operate under, as revealed by your question, would be virulently opposed by the vast majority of academics. You might get a sense of that from the other responses here.

I have come across a number of researchers who share your views. They feel that 'doing research' is more important than writing about it, and time spent writing is time wasted (especially introduction and such). This question here borders on such thinking.

It's absolutely untrue that writing is less important. This may be a shield to cover up lack of clarity or less critical, inadequate language skills. You should introspect on whether this is the case at your group.

If you want to hire people for money to write for you, those people are likely to be students looking to supplement their income or pay off a loan. The arrangement would probably work, but some people would find this exploitative, like a very mild version of a sweatshop.

If you want to have these writers work for authorship, you are going down a very slippery slope. What happens if the writer disagrees with your research? What if they want to add something of their own? It's quite natural to develop a sense of ownership and accountability after some time; how would you deal with that? How do you 'fire' these people without them raising misconduct claims? Note that I'm on pointing out practical difficulties, the ethical considerations that make this a bad idea should already be quite clear to you.

In summary, my advice is, don't. Make time to write, or wait till you have some downtime to write.